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Local and global synchronization in general

Local and global synchronization in general complex dynamical networks with delay coupling

Jianquan Lu,Daniel W.C.Ho

Department of Mathematics,City University of Hong Kong,83Tat Chee Avenue,Kowloon,Hong Kong,China

Accepted 25October 2006

Communicated by Prof.M.S.El Naschie

Abstract

Local and global synchronization of complex dynamical networks are studied in this paper.Some simple yet generic criteria ensuring delay-independent and delay-dependent synchronization are derived in terms of linear matrix inequal-ities (LMIs),which can be veri?ed easily via interior-point algorithm.The assumption that the coupling con?guration matrix is symmetric and irreducible,which is frequently used in other literatures,is removed.A network with a ?xed delay and a special coupling scheme is given as an example to illustrate the theoretical results and the e?ectiveness of the proposed synchronization scheme.

1.Introduction

Over the past ten years,there has been much activity studying the topology and dynamical behavior of complex net-works across many ?elds of science and engineering [1–29].A complex network is a large set of interconnected nodes,in which a node is a fundamental unit,that can have di?erent meaning in di?erent situations.Many real-world complex networks often display better cooperative or synchronous behaviors among their constituents,such as the synchronous phenomena on the Internet,synchronous transfer of digital or analog signals in communication networks,and biolog-ical neural networks are also closely relating with synchronization [3–5].There are many bene?ts of having synchroni-zation in engineering application,such as secure communication and harmonic oscillation generation [5,6].However,there are also harmful synchronization to be eliminated,for instance,periodic routing messages from di?erent routers can be synchronized,which will lead to congestion in the network data tra?c.Hence,study of synchronization in com-plex networks is very interesting and important both in theory and application.

Before the year 1998,synchronization in large-scale networks of coupled systems were mainly focused on completely regular networks and randomly coupled networks,such as the continuous cellular neural network and the discrete cou-pled map lattice,and so on,while most of the real-world networks are neither completely regular nor completely ran-0960-0779/$-see front matter ó2006Elsevier Ltd.All rights reserved.doi:10.1016/j.chaos.2006.10.030

q This work was supported by HKSRA RAG CityU 101004and CityU SRG 7001982.*

Corresponding author.

E-mail address:madaniel@https://www.sodocs.net/doc/559556711.html,.hk (D.W.C.Ho).

Available online at https://www.sodocs.net/doc/559556711.html,

Chaos,Solitons and Fractals 37(2008)

1497–1510

https://www.sodocs.net/doc/559556711.html,/locate/chaos

dom.However,this condition has recently been changed due to the introduction of small-world and scale-free network models.Watts and Strogatz (WS)[1]introduced the concept of small-world network model to describe a transition from a regular lattice to a random graph,which exhibits simultaneously a high degree of clustering as in the regular networks and a small average distance between two nodes as in the random networks.To explain the origin of power-law degree distribution of real-world networks,Barabasi and Albert [2]proposed a scale-free network model,which is in-homogeneous in nature,that is,most nodes have very few connections but a small number of particular nodes have many connections.

Recently,Wang and Chen [17,18]introduced a simple uniform model and investigate its synchronization criteria in small-world and scale-free networks.Lu ¨and Chen [19]presented a time-varying complex dynamical network model,and investigated its synchronization phenomenon by proving several network synchronization theorems.Li and Chen [20]introduced a complex dynamical network model with coupling delays,and derived some synchronization condi-tions for both delay-independent and delay-dependent asymptotical stabilities.By utilizing Lyapunov functional method,Cao et al.[23]derived some su?cient conditions for the global exponential synchronization in arrays of cou-pled delayed neural networks.Li et al.[25]investigated the global synchronization of a class of complex networks with time-varying delays,where delay appeared in the isolate systems but not in the coupling term.Checco et al.[26]studied the synchronization of random networks with given expected degree sequences,and showed that random graphs almost surely synchronize.Lu and Chen [9]discussed local and global synchronization for linearly coupled ordinary di?erential systems with the coupling matrix not assumed to be symmetric or irreducible.

One should note that,while some su?cient criteria have been proposed to ensure synchronization of dynamical net-works in the above literatures which are convenient to verify in practice,most of them have neglected the e?orts of time-delay and/or the asymmetry and reducibility of coupling matrix for real-world networks.However,in reality,there usu-ally are some delays in spreading and response due to the ?nite speeds of transmission and spreading as well as tra?c congestion.Therefore,in order to stimulate more realistic networks,one should introduce time-delays to the dynamical networks while modeling [20].The assumption appeared in most of literatures that the coupling matrix is symmetric and irreducible is also not coincident with the fact in real-life networks.In this paper,as in [9],the state space of the network is decomposed into two parts:synchronization manifold S and its transverse space,then the synchronization of dynam-ical networks could be transformed into the stability of the synchronization manifold S .Under this decomposition,we study the synchronization properties of complex delayed dynamical networks with asymmetric and reducible coupling matrix.By utilizing the Lyapunov–Krasovskii functional method,some local synchronization criteria for both delay-independent and delay-dependent stabilities are derived in terms of linear matrix inequalities (LMIs).In addition,we obtain some global synchronization conditions for the delayed dynamical networks.

The rest of this paper is organized as follows.In Section 2,a complex delayed dynamical network model is presented and some preliminaries are introduced.In Section 3,both delay-independent and delay-dependent stability criteria of the synchronization manifold S are studied for the delayed coupled network with asymmetric coupling topology.In Section 4,global stability conditions of the synchronization manifold are presented for dynamical networks respectively with irreducible and reducible coupling matrices.In Section 5,numerical simulations are given to verify the proposed theoretical results.In Section 6,we conclude this paper.

Throughout this paper,for real symmetric matrices X and Y ,the notation X P Y (respectively,X >Y )means that the matrix X àY is positive semi-de?nite (respectively,positive de?nite);I n is the identity matrix of order n .R denote the set of real numbers;R n ?R ?R ?...?R |????????????{z????????????}

;R n ?n are n ·n real matrices;The superscript ‘‘T’’represents the trans-pose;matrices,if not explicitly stated,are assumed to have compatible https://www.sodocs.net/doc/559556711.html,work model and preliminaries

Consider a dynamical network consisting of N identical nodes with di?usive and delay coupling,in which each node is an n -dimensional dynamical system.The mathematical model of the coupled network can be described by the follow-ing functional di?erential equations [20]:

i et T?f ex i et TTtX N j ?1

a ij C x j et às T;i ?1;2;...;N ;e1T

where f :R n !R n is a continuously di?erentiate function,x i et T?ex i 1et T;x i 2et T;...x in et TTT 2R n are the state variables of node i ,s is the coupling delay,C is the inner coupling matrix between two connected nodes,A =[a ij ]N ·N represents the outer coupling con?guration of the complex network,where a ij is de?ned as follows:if there is a connection from node j to node i (i 5j ),a ij >0;otherwise a ij =0(i 5j ),and a ii ?àP N j ?1j ?i

a ij for i =1,2,...,N .Note that the symmetry restric-1498J.Lu,D.W.C.Ho /Chaos,Solitons and Fractals 37(2008)1497–1510

tion on the coupling matrix,that is a ij =a ji (i 5j ),is removed here.The di?usive coupling con?guration means that these connected nodes would be decoupled at the synchronized state.Time delays are added into the model,since there are usually some time delays in in?uence and response in reality due to the ?nite speeds of transmission and spreading as well as tra?c congestions.

De?nition 1.Synchronization manifold S ?fex T 1et T;x T 2et T;...;x T

N et TTT 2R nN :x i et T?x j et Tfor i ,j =1,2,...,N },where x i (t )=(x i 1(t ),x i 2(t ),...,x in (t ))T

(i =1,2,...,N )is the state of node i .

De?nition 2.Synchronization manifold S is said to be locally asymptotically stable for the complex dynamical network (1),that is the complex dynamical network (1)is locally asymptotically synchronized if for any r 2R , >0,there exists d =d (r , )such that k x i (0)àx j (0)k 6d implies k x i (t )àx j (t )k 6 (i ,j =1,2,...,N )for t P r ,and there is a b 0=b 0(r )>0such that k x i (0)àx j (0)k 6b 0implies k x i (t )àx j (t )k !0(i ,j =1,2,...,N )as t !1.

De?nition 3.Synchronization manifold S is said to be globally asymptotically stable for the complex dynamical net-work (1),that is the complex dynamical network (1)is globally asymptotically synchronized if for any r 2R ; >0,there exists d =d (r , )such that k x i (0)àx j (0)k 6d implies k x i (t )àx j (t )k 6 (i ,j =1,2,...,N )for t P r ,and k x i (t )àx j (t )k !0(i ,j =1,2,...,N )as t !1hold for any initial conditions x i (0)and x j (0)(i =1,2,...,N ).

De?nition 4([8,9]).Function class QUAD(D ,P ):let P =diag{p 1,p 2,...,p n }be positive de?nite diagonal matrix and D =diag{d 1,d 2,...,d n }be a diagonal matrix.QUAD(D ,P )denotes a class of continuous functions f ex ;t T:R n ?0;t1?T!R n satisfying (x ày )T P [(f (x )àf (y ))+D (x ày )]6àf (x ày )T (x ày )for some f >0,all x ;y 2R n and t >0.De?nition 5.Matrix A ?ea ij TN ?N 2R N ?N is said to belong to A 1,if (i)a ij P 0ei ?j T;a ii ?à

P N

j ?1j ?i

a ij ,for i =1,2,...,N ;

(ii)real parts of eigenvalues of A are all negative except an eigenvalue 0with multiplicity 1.

De?nition 6.Matrix A ?ea ij TN ?N 2R N ?N is said to belong to A 2,if (i)a ij P 0,i 5j ,a ii ?àP N

j ?1j ?1

a ij ,for i =1,2,...,N ;

(ii)A is irreducible.

Lemma 1([9,30]).If A 2A 1,then the following are valid:

(i)If k is an eigenvalue of A and k 50,then Re (k )<0;

(ii)A has an eigenvalue 0with multiplicity 1and the right eigenvector [1,1,...,1]T ;(iii)Suppose n ??n 1;n 2;...;n N T 2R N (without loss of generality,assume P N i ?1n i ?1)is the left eigenvector of A cor-responding to eigenvalue 0.Then,n i P 0hold for all i =1,2,...,N;(iv)In addition,A 2A 2if and only if n i >0for all i =1,2,...,N;

(v)A is reducible if and only if for some i ,n i =0.In such a case,by a suitable rearrangement,assume that

n T ??n T t;n T 0 T ,where n t??n 1;n 2;...;n p T 2R p

with all n i >0,i =1,2,...,p ,and n 0??n p t1;n p t2;...;n N 2R N àp with all n j =0,j =p +1,p +2,...,N .Then A can be rewritten as

A 11A 12

A 21A 22

,where A 222R pp is irreduc-ible and A 21=0.

Lemma 2(Lyapunov–Krasovskii Stability Theorem [31,32]).Consider the delayed differential equation

et T?f et ;x t T:Suppose that f is continuous and f :R ?C !R n takes R ?(bounded sets of C)into bounded sets of R n ,and u ;v ;w :R t!R tare continuous and strictly monotonically non-decreasing functions,u(s),v(s),w(s)are positive for s >0with u(0)=v(0)=0.If there exists a continuous functional V :R ?C !R such that

J.Lu,D.W.C.Ho /Chaos,Solitons and Fractals 37(2008)1497–15101499

u ek x et TkT6V et ;x et TT6v ek x et TkT;_V

et ;x et TT6àw ek x et TkT;where _V

is the derivative of V along the solution of the above delayed differential equation,then the solution x =0of this equation is uniformly asymptotically stable.

Lemma 3(Scalar complement:Boyd et al.[33]).The following linear matrix inequality (LMI)

Q ex TS ex T

S T ex TR ex T

!>0;

where Q(x)=Q T (x),R(x)=R T (x),and S(x)depend af?nely on x,is equivalent to one of the following conditions (i)R (x )>0,Q (x )àS (x )R à1(x )S T (x )>0;(ii)Q (x )>0,R (x )àS T (x )Q à1(x )S (x )>0.

Lemma 4(Moon et al.[34]).Assume that a eáT2R n a ;b eáT2R n b and M eáT2R n a ?n b are de?ned on an interval X .Then,for any matrices X 2R n a ?n a ;Y 2R n a ?n b and Z 2R n b ?n b ,the following inequality holds:

à2Z

X a T ea TMb ea Td a 6

Z X a ea Tb ea T !T X Y àM Y T àM T Z !a ea T

b ea T !d a ;e2Twhere

Y Y T

Z !

P 0:

3.Local synchronization criteria

In this section,local synchronization criteria for both delay-independent and delay-dependent asymptotically stabil-ities will be discussed.

Suppose n ??n 1;n 2;...;n N T 2R N

is the normalized left eigenvector of coupling con?guration matrix A ,that is P N i ?1n i ?1.Following [9],we de?ne x et T?P

N i ?1n i x i et T,and X et T??

x T et T; x T et T;...; x T et T T 2S ,which can be regarded as a projection of network’s state x et T??x T 1et T;x T 1et T;...;x T

N et T on the synchronization manifold S .The dynamics of the state x et Tcan be described by the following equation:

_ x

et T?X N i ?1

n i _x i et T?

X N i ?1

n i ?f ex i et TTt

X N j ?1

a ij C x j et às T ?

X N i ?1

n i f ex i et TTt

X N j ?1

x j et às T

X N i ?1

n i a ij C ?

X N i ?1

n i f ex i et TT:

e3T

Theorem 1.Consider the complex delayed dynamical network (1)with coupling matrix A 2A 1.Let k 2,k 3,...,k l be the non-zero eigenvalues of the coupling con?guration matrix A which may be complex.If the following l à1of n-dimensional delayed differential equations are asymptotically stable about their zero solutions:

i et T?R et Tu i et Ttk i Cu i et às T;i ?2;3;...;l

e4T

then the synchronization manifold S is locally asymptotically stable.

Proof.Let e i et T?x i et Tà

x et T;i ?1;2;...;N ,then e i (t )belongs to the transverse space of synchronization manifold S .Therefore,the synchronization of complex delayed dynamical networks (1)is equivalent to e i (t )!0as t !1,i =1,2,...,N .It follows from the differentiability of function f that

_e i et T?R et Te i et Tt

X N j ?1

a ij C e j et às T;i ?1;2;...;N ;e5T

1500J.Lu,D.W.C.Ho /Chaos,Solitons and Fractals 37(2008)1497–1510

where RetT?Dfe xetTT2R n?n is the Jacobian matrix of f(x(t))at xetT.Let eetT??e1etT;e2etT;...;e NetT 2R n?N,we can obtain

_eetT?RetTeetTtC eetàsTA T:e6TBy matrix theory[30],we have the following Jordan decomposition for matrix A:A T=U J Uà1,where J= diag{J1,J2,...,J l}is a block diagonal matrix,and J k is the Jacobian block corresponding to the m k multiple eigenvalue

k k of A:

k k10ááá00

0k k1ááá00

...........

000ááá0k k

m k?m k

.Assume that k1=0,then one can obtain that J1is a number by Lemma1.It is

clear that the?rst column n=[n1,n2,...,n N]T of U is the left eigenvector corresponding to eigenvalue0(assume that

P N

i?1n i?1)and the?rst row of Uà1is the right eigenvector[1,1,...,1]T corresponding to eigenvalue0.

Now let u(t)=e(t)U,then we can obtain_uetT?RetTuetTtCuetàsTJ,where uetT??u1etT;u2etT;...;u letT ;u ketT

??u k

1etT;u k

etT;...;u k

m k

etT ,and u k

etT2R n for16i6m k.For k=1,since the?rst column n=[n i,n2,...,n N]T of U is

the left eigenvector corresponding to eigenvalue0,we have u1etT?P N

i?1

e ietTn i?

P N

i?1

n i?x ietTà xetT ?

P N

i?1

n i x i

etTà xetT?0.For k=2,3,...,l,we obtain that

_u k

1etT?RetTu k

etTtk k Cu k

etàsT;e7T

_u k

p etT?RetTu k

etTtk k Cu k

etàsTtCu k

pà1

etàsTfor p?2;3;...;m k:e8T

By the conditions of this theorem,one can obtain that u k

1?oe1Tfor k=2,3,...,https://www.sodocs.net/doc/559556711.html,bining this with(8),we have

u k

p ?oe1Tfor p=2,3,...,m k by induction.Hence,one can have u k(t)=o(1)for k=2,3,...,https://www.sodocs.net/doc/559556711.html,bined with

u1(t)=0,we have u(t)=o(1).Therefore,e(t)=u(t)Uà1=o(1),and then the synchronization manifold S for dynam-ical system(1)is locally asymptotically stable.This completes the proof.h

Let k i=a i+j b i(i=2,3,...,l),and u i(t)=u i(t)+j v i(t)(i=2,3,...,l)be the solution of system(4),in which j is the imaginary unit,u i(t)=[u i1(t),u i2(t),...,u in(t)]T and v i(t)=[v i1(t),v i2(t),...,v in(t)]T for i=2,3,...,l,then we have _u ietT?RetTu ietTta i C u ietàsTàb i C v ietàsT;

_v ietT?RetTv ietTta i C v ietàsTtb i C u ietàsT;i?2;3;...;l:

e9T

Let w ietT?u ietT

v ietT

ei?2;3;...;lT;R?etT?

RetT0

0RetT

ei?2;3;...;lT,and K i?

a i Cà

b i C

b i C a i C

,it follows from(9)

that

_w ietT?R?etTw ietTtK i w ietàsT;i?2;3;...;l:e10T

Theorem2.Suppose A2A1.If there exist two series of positive de?nite matrices P i and Q i(i=2,3,...,l),such that P i R?etTtR T

etTP itQ i P i K i

K T

i P iàQ i

<0;for i?2;3;...;le11Tthen the synchronization manifold S is locally asymptotically stable for any?xed delay s>0.

Proof.In order to prove the asymptotical stability of the synchronization manifold,consider the following Lyapunov–Krasovskii type functional:

V ietT?w T

i etTP i w ietTt

Z t

tàs

w T

eaTQ i w ieaTd ae12T

Calculating the time derivative of the functional(12)along the trajectory of system(10),we can obtain

_V i etT?2w T

etTP i_w ietTtw T

etTQ i w ietTàw T

etàsTQ i w ietàsT

?w T

etT?P i R?etTtR T

etTP itQ i w ietTt2w T

etTP i K i w ietàsTàw T

etàsTQ i w ietàsT

6w T

etT?P i R?etTtR T

etTP itQ itP i K i Qà1

K T

P i w ietT:e13TJ.Lu,D.W.C.Ho/Chaos,Solitons and Fractals37(2008)1497–15101501

From the Schur complements,the LMIs (11)are equivalent to P i R ?et TtR T ?et TP i tQ i tP i K i Q à1i K T

i P i <0for

i =2,3,...,l .Therefore,_V

i et Tis negative de?nite for i =2,3,...,l .From Lemma 2,we can obtain that system (10)is asymptotically stable.That is w i (t )!0as t !1,then we have u i (t )=u i (t )+jv i (t )!0as t !1.Therefore,by The-orem 1,the synchronization manifold S of complex delayed dynamical network (1)is locally asymptotically stable for any ?xed delay s >0.This ends the proof of this theorem.h

Remark 1.Theorem 2in [20]is a special case of Theorem 2in this paper.One can obtain Theorem 2in [20]by assuming b i =0and v i (t )=0,since only networks with symmetric coupling matrix are discussed in [20].Corollary 1.Suppose A 2A 1.If there exist two positive de?nite matrix P and Q,such that P R ?et TtR T ?et TP tI tk 2

max P C ?P <0;

e14T

where k max ,max fj k i j :i ?2;3;...;l g ?max ???????????????a 2i tb 2

i q :i ?2;3;...;l &'

and C ??CC T 0

CC T

,then the synchroni-zation manifold S is locally asymptotically stable for any ?xed delay s >0.

Proof.Take Q i =I n (i =2,3,...,l )in Theorem 2,then the LMI (11)is equivalent to P R ?et TtR T ?et TP tI tea 2

i tb 2i TP C ?P <0for i =2,3,...,l .Since

P R ?et TtR T ?et TP tI tea 2i tb 2i TP C ?P 6P R ?et TtR T

?et TP tI tk 2max P C ?P <0

and the conditions in Theorem 2is satis?ed.The proof is ended.h

The criterion given in Theorem 2is delay-independent,which does not include any information on the size of delay.However,it is known that delay-dependent synchronization conditions are generally less conservative than delay-inde-pendent ones especially when the size of the delay is small.In the following,some delay-dependent criteria for the syn-chronization of the network with delayed coupling will be given,which employ the information about time delay.Theorem 3.The synchronization manifold S is asymptotically stable for any ?xed time-delay s satisfying s 2?0; s ,if there exist matrices P i >0,Q i >0,Z i >0,X i ,Y i (i =2,3,...,l)with relevant dimensions such that the following conditions hold:

D ?P i R ?et TtR T ?et TP i t s X i tY i tY T

tQ i P i K i àY i s R T ?et TZ i K T i P i àY T

i àQ i s K T i Z i s Z i R ?et T s Z i K i à s Z i 264375

<0for i ?2;3;...;l ;e15Twhere

X i

Y i

Y T i

Z i

P 0for i ?2;3;...;l :e16T

Proof.Consider the following Lyapunov functional:

V i et T?V i 1et TtV i 2et TtV i 3et T;e17T

where

V i 1et T?w T i et TP i w i et T;

V i 2et T?Z 0às Z t

t tb

_w T i ea TZ i _w i ea Td a d b ;V i 3et T?

w T i ea TQ i w i ea T:

By the Newton–Leibniz formula,one can obtain that

x et às T?x et Tà

Z t

t às

_x ea Td a and therefore,the derivative of V i 1(t )satis?es

i 1et T?2w T i et TP i _w

i et T?

w T i et T?P i eR ?et T

tK i TteR ?et TtK i TT

P i w i et Tà

2w T i et TP i K i

t às

_w i ea Td a :e18T

Now,applying Lemma 4to (18)gives (16)and that

1502J.Lu,D.W.C.Ho /Chaos,Solitons and Fractals 37(2008)1497–1510

_V i1etT6w T

etT?P ieR?etTtK iTteR?etTtK iTT P i w ietTts w T

etTX i w ietTt2w T

etTeY iàP i K iT

Z t tàs _w ieaTd at

Z t

tàs

_w T

eaTZ i_w ieaTd a6w T

etT?P i R?etTtR T

etTP it s X itY T

tY i w ietTt2w T

etT?P i K iàY i w ietàsT

Z t

tàs _w T

eaTZ i_w ieaTd a:e19T

Moreover,

_V i2etT?

às

?_w T

etTZ i_w ietTà_w T

ettbTZ i_w iettbT d b

?s?R?etTw ietTtK i w ietàsT T Z i?R?etTw ietTtK i w ietàsT à

Z t

tàs

_w T

eaTZ i_w ieaTd a

6 s?R

etTw ietTtK i w ietàsT T Z i?R?etTw ietTtK i w ietàsT à

Z t

tàs

_w T

eaTZ i_w ieaTd a;e20T

and

_V i3etT?w T

etTQ i w ietTàw T

etàsTQ i w ietàsT:e21T

Therefore,

_V i etT?_V i1etTt_V i2etTt_V i3etT6

w ietT

w ietàsT

!T?

?i2

s K T

Z i K iàQ i

etT

w ietàsT

;e22T

where

?i1?P i R?etTtR T

?etTP it s X itY itY T

tQ it s R T

etTZ i R?etT;

?i2?P i K iàY it s R T

etTZ i K i:

By utilizing Lemma3,we can easily verify that(15)is equivalent to the following inequality:?i1?i2

i2 s K T

Z i K iàQ i

<0:e23T

Hence,_V ietTis negative de?nite.By Lemma2and Theorem1,one can obtain that the synchronization manifold S is asymptotically stable for any?xed time-delay s satisfying s2?0; s .This ends the proof.h

Theorem4.Suppose that the constant time-delay s2?0; s for some s<1.If there exist matrices P i>0,Q i>0,Z i>0, F i,H i(i=2,3,...,l)with relevant dimensions such that the following LMIs hold:

P i R?etTtR T

etTP itF itF T

tQ i P i K iàF itH T

à s F i s R?etTZ i

K T

P iàF T

tH iàH iàH T

àQ ià s H i s K T

Z i

à s F T

à s H T

à s Z i0

s Z i R T

etT s Z i K i0à s Z i

75<0for i?2;3;...;le24T

then the synchronization manifold S is asymptotically stable for any?xed time-delay s2?0; s .

Proof.Consider the same Lyapunov functional as Theorem3,and calculate the time derivative of V i(t)along the tra-jectory of(10),we obtain

_V i1etT?2w T

etTP i?R?etTw ietTtK i w ietàsT

?2w T

etTP i?R?etTtK i w ietTà2w T

etTP i K i

Z t

tàs

_w ieaTd a

?2w T

etTP i?R?etTtK i w ietTt2w T

etTeF iàP i K iT

Z t

tàs

_w ieaTd a

t2w T

etàsTH i

Z t

tàs

_w ieaTd aà2w T

etTF i

Z t

tàs

_w ieaTd a

à2w T

etàsTH i

Z t

tàs

_w ieaTd a

J.Lu,D.W.C.Ho/Chaos,Solitons and Fractals37(2008)1497–15101503

Z t

tàs

2w T

etTeP i R?etTtF iTw ietTt2w T

etTeP i K iàF itH T

Tw ietàsT?á

à2w T

i etàsTH i w ietàsTà2s w T

etTF i_w ieaTà2s w T

etàsTH i_w ieaT

;

_V i2etT?

às

?_w T

etTZ i_w ietTà_w T

ettbTZ i_w iettbT d b

Z t

tàs

?_w T

etTZ i_w ietTà_w T

eaTZ i_w ieaT d a

Z t

tàs

eR?etTw ietTtK i w ietàsTTT Z ieR?etTw ietTtK i w ietàsTTà_w T

eaTZ i_w ieaT

h i

d a

Z t

tàs

s w T

etTR T

etTZ i R?etTw ietTt2s w T

etTR T

etTZ i K i w ietàsT

ts w T

etàsTK T

Z i K i w ietàsTàs_w T

eaTZ i_w ieaT

d a

and

_V i3etT?w T

etTQ i w ietTàw T

etàsTQ i w ietàsT?

Z t

tàs

w T

etTQ i w ietTàw T

etàsTQ i w ietàsT

d a:

Therefore,

_V i etT?_V i1etTt_V i2etTt_V i3etT?

Z t

tàs

w ietT

w ietàsT

_w ieaT

T W

W i2às F i

W T

W i3às H i

às F T

às H T

às Z i

w ietT

w ietàsT

_w ieaT

75d ae25T

where

W i1?P i R?etTtR T

?etTP itF itF T

tsR T

etTZ i R?etTtQ i;

W i2?P i K iàF itH T

tsR?etTZ i K i;

W i3?àH iàH T

i tsK T

Z i K iàQ i:

By Lemma3,it follows from Z i>0that the inequality

D1?

W i1W i2às F i

W T

W i3às H i

às F T

às H T

às Z i

75<0e26T

is equivalent to the following inequality:

D26W i1W i2

W T

W i3

F i

H i

Zà1

F T

H T

W i1ts F i Zà1

F T

W i2ts F i Zà1

H T

W T

ts H i Zà1

F T

W i3ts H i Zà1

H T

<0:

Also by Lemma3and inequality(24),we have

D3?

P i R?etTtR T

etTP itF itF T

tQ i P i K iàF itH T

K T

P iàF T

tH iàH iàH T

àQ i

t s

àF i R?etTZ i

àH i K T

Z i

!Zà1

0Zà1

àF T

àH T

Z i R T

etTZ i K i

<0for i?2;3;...;l:e27T

Hence,we have D26D3<0,and then_V ietTis negative de?nite.Therefore,by Lemma2and Theorem1,we have that the synchronization manifold S is asymptotically stable for any?xed time-delay s satisfying s2?0; s .This completes the proof of this theorem.h

Remark2.The delay-dependent synchronization criterion in Theorem4is less conservative than previous one in The-orem3.Some bounding techniques,which were previously utilized to deal with the weighted cross-products of the state and the delayed state,are not used in deriving this delay-dependent synchronization result.This is?rstly stated in[12]. Remark3.While several delay-independent and delay-dependent criteria ensuring the synchronization of dynamical networks(1)are given in Theorems2–4,it is easy to see that a prerequisite requirement is that the dynamics of isolate node is stable.Therefore,they are not available for dynamical networks with periodic or chaotic isolate nodes.

1504J.Lu,D.W.C.Ho/Chaos,Solitons and Fractals37(2008)1497–1510

4.Global synchronization criteria

In previous section,local stability of the synchronization manifold was analyzed,and several su?cient conditions were given to guarantee that the trajectory of delayed dynamical networks will come to the synchronization manifold S under small variation.However,it is more interesting to study the global synchronization for dynamical networks(1), that is,whether the trajectory of networks converge to the manifold S for any initial conditions.In this section,we will give some global stability criteria for synchronization manifold S when the coupling con?guration matrix A is irreduc-ible or reducible.We will?rstly give a criterion to ensure the global synchronization of delayed dynamical network with irreducible coupling matrix,which will be generalized to the case of reducible coupling matrix.

Theorem 5.Suppose that A2A2,f2QUAD(D,P),and the inner coupling matrix C=diag{c1,c2,...,c n}.Let N=diag{n1,n2,...,n N},where[n1,n2,...,n N]T is the left eigenvector corresponding to eigenvalue0.If there exists diagonal positive de?nite matrix Q=diag{q1,q2,...,q n},such that

eàfàp j d jtq jTN1p j c j N A

j c

A T Nàq

<0;for j?1;2;...;ne28Tthen the synchronization manifold S is globally asymptotically stable for the complex delayed dynamical network(1). Proof.De?ne e ietT?x ietTà xetT.By Eq.(3),we can obtain

_e ietT?_x ietTà_ xetT?fex ietTTt

X N

j?1a ij C x jetàsTà

X N

k?1

n k fex ketTTt

X N

l?1

a kl C x letàsT

?fex ietTTà

X N

k?1n k fex ketTTt

X N

j?1

a ij C e jetàsT

?fex ietTTàfe xetTTt

X N

j?1a ij C e jetàsTtfe xetTTà

X N

k?1

n k fex ketTT

:e29T

De?ne a Lyapunov–Krasovski functional candidate for these error systems(29)as

VetT?V1etTtV2etT;e30Twhere

V1etT?

1X N

i?1n i e T

etTPe ietT;

V2etT?

X N

i?1n i

Z t

tàs

e T

etTQe ietT:

The derivative of V1(t)and V2(t)along the trajectories of the error systems(29)can be respectively calculated as follows:

_V 1etT?

X N

i?1

n i e T

etTP_e ietT?

X N

i?1

n i e T

etTP fex ietTTàfe xetTTt

X N

j?1

a ij C e jetàsTtfe xetTTà

X N

k?1

n k fex ketTT

"#?

X N

i?1

n i e T

etTP fex ietTTàfe xetTTtDex ietTà xetTTt

X N

i?1

a ij C e jetàsTàD e ietT

X N

i?1

n i e T

etTP fe xetTTà

X N

k?1

n k fex ketTT

According to De?nition4and P N

t?1

n i e T

etT?0,for some f>0,we have

_V 1etT6àf

X N

i?1

n i e T

etTe ietTt

X N

i?1

n i e T

etTP

X N

j?1

a ij C e jetàsTà

X N

i?1

n i e T

etTP D e ietT

?à

X n

j?1

f~e jetTT N~e jetTt

X n

j?1

~e jetTT N A~e jetàsTà

X N

j?1

d j~

e jetTT N~e jetT

J.Lu,D.W.C.Ho/Chaos,Solitons and Fractals37(2008)1497–15101505

and

_V 2et T?

X N i ?1

n i ?e T i et TQe i et T

e T i et

às TQe i et às T ?X

n j ?1

?q j ~e j et TT N ~e j et Tàq j ~e j et às TT N ~e j et às T :

e31T

where ~e j et T??e j 1et T;e j 2et T;...;e j N et T T ,and e i et T??e 1i et T;e 2i et T;...;e n

i et T T .Thus,we can obtain

et T6X n j ?1

~e j et TT eàf àp j d j tq j TN ~e j et Tàp j c j ~e j et TT N ~e j et às Tàq j ~e j et às TT N ~e j

et às Th i ?X n j ?1~e j et T

~e j et às T !T eàf àp j d j tq j TN 1

2p j c j

N A 1

2p j c j

A T N àq j N

"#~e j et T~e j et às T

<0:e32T

Therefore,by Lemma 2,the synchronization manifold S is globally asymptotically stable for the complex delayed

dynamical network (1)with irreducible coupling matrix.This completes the proof.h

In the following,we discuss the case where A 2A 1.Without loss of generality,reducible matrix A 2A 1can be writ-ten as A ?A 11A 12áááA 1p 0A 22áááA 2p ...........

.00...A pp 2666643

775;e33Twhere A pp 2R m p ;m p is irreducible,and A qq 2R m q ;m q for q =1,2,...,p .Since A belongs to A 1,for each q ,there must exist

k >q such that A qk 50[9,24].

Let N q ?P q k ?1m k .Then the complex delayed dynamical network (1)can be decomposed into q subsystems denoted by S q ?f N q à1t1;N q à1t2;...;N q g for q =1,2,...,p ,with N 0=0

S p :_x

i et T?f ex i et TTtX

j 2S p

a ij C x j et às T;i 2S p e34Tand

S p :_x

i et T?f ex i et TTtX

j 2S q

a ij C x j et às Tt

r 2S k

k >q

a ir C x r et às T;i 2S q ;q ?1;2;...;p à1:e35T

If the subsystems S k ;k ?p ;p à1;...;q t1,are globally synchronized,then these subsystems are decoupled,and the synchronized state x *(t )satis?es the following equation:

?et T?f ex ?et TT:e36TTherefore,according to the zero-sum rows,i.e.,P j 2S q a ij tP

r 2S k k >q

a ir ?0for i 2S q ,the next coupled subsystem S q can

be described by the following equations:

i et T?f ex i et TTtX j 2S q

a ij C x j et às TtX r 2S k

k >q

a ir C x r et às T?f ex i et TTtX j 2S q

a ij C x j et às TtX

r 2S k k >q

a ir C x ?et às T?f ex i et TTt

j 2S q

a ij C x j et às Tà

j 2S q

a ij C x ?et às T?f ex i et TTt

j 2S q

a ij C e j et às T;i 2S q e37T

and then

_e i et T?f ex i et TTàf ex ?et TTtX

j 2S q

a ij C e j et às T;i 2S q ;e38T

where e i (t )=x i (t )àx *(t )for i 2S q .

Hence,we can study the global stability of the synchronization manifold S by ?rstly investigating the synchroniza-tion of the subsystem S p with irreducible coupling matrix A pp ,and secondly studying the following subsystems (38)step by step.The following theorem will show a synchronization criterion for complex delayed dynamical networks with reducible coupling con?guration matrix using this process.

1506J.Lu,D.W.C.Ho /Chaos,Solitons and Fractals 37(2008)1497–1510

Theorem6.Suppose that A2A1,f2QUAD(D,P),and the inner coupling matrix C=diag{c1,c2,...,c n}.If there exists diagonal positive de?nite matrices Q q=diag{q q1,q q2,...,q qn}(q=1,2,...,p),such that the following two series matrix inequalities hold:

eàfàp j d jtq pjTN p1p j c j N p A pp

j c

A T

N pàq pj N p

<0;for j?1;2;...;n;e39Twhere n p?f n p1;n p2;...;n pmp g2R mp is the left eigenvector of the matrix A pp corresponding to eigenvalue0satisfying

P m p

k?1n pk?1,and N p?diag f n p1;n p2;...;n pm

2.The following matrix inequalities hold for each q=1,2,...,pà1

eàfàp k d ktq qkTI m

q 1p

c k A pp

k c k A T

àq qk I m

<0;for k?1;2;...;ne40Tthen the complex delayed dynamical network(1)with reducible and asymmetric coupling matrix A is globally asymptoti-cally synchronized.

Proof.By Theorem5,it is easy to check that the?rst series of matrix inequalities can ensure that subsystem S pp,with irreducible matrix can be globally asymptotically synchronized to x*(t).Therefore,the rest work is to prove that the second series matrix inequalities would lead to e ietT?x ietTàx?etT!0ei2S qTas t!1for q=1,2,...,pà1.

Choose the following Lyapunov functional:

VetT?1

i2S q

e T

etTPe ietTt

i2S q

Z t

tàs

e T

etTQ q e ietT:

Calculating the time derivative of this Lyapunov function along the trajectory of system(38)gives that

_VetT?

i2S q e T

etTP_e ietTt

i2S q

?e T

etTQ q e ietTàe T

etàsTQ q e ietàsT ?

i2S q

e T

etTP?fex ietTTàfex?etTT

j2S q a ij C e jetàsT t

i2S q

?e T

etTQ q e ietTàe T

etàsTQ q e ietàsT ?

i2S q

?e T

etTP?fex ietTTàfex?etTTtD e ietT

i2S q X

j2S q

?àe T

etTP D e ietTta ij e T

etTP C e ietàsT t

i2S q

?e T

etTQ q e ietTàe T

etàsTQ q e ietàsT 6àf

i2S q

e ietTT e ietT

X n

k?1

àp k d k~e ketTT~e ketTtp k c k~e ketTT A qq~e ketàsT

tq qk~e ketTT~e ketTàq qk~e ketàsTT~e ketàsT

X n

k?1

eàfàp k d ktq qkT~e ketTT~e ketTtp k c k~e ketTT A qq~e ketàsT

àq qk~e ketàsTT~e ketàsT

~e ketT

~e ketàsT

"#Teàfàp

d ktq qkTI m

c k A qq

A T

àq qk I m

~e ketT

~e ketàsT

<0:e41T

Hence,_VetTis negative de?nite.It follows from Lemma2that the subsystems S qeq?1;2;...;pà1Tcan also be glob-ally asymptotically synchronized to x*(t).Therefore,the whole complex delayed dynamical network(1)with irreducible and asymmetric coupling matrix A is globally asymptotically synchronized.This theorem is proved.h

5.Numerical simulations

From the proof of the theorems,one can obtain that the above-derived synchronization criteria are available for networks with di?erent topologies and sizes.In this subsection,a lower-dimensional network model with?ve nodes J.Lu,D.W.C.Ho/Chaos,Solitons and Fractals37(2008)1497–15101507

is used as an example to illustrate the main theoretical result.Each node in the network is a simple two-order stable linear system described by

_x 1et T_x 2et T

"#?à6x 1et Tà7x 2et T

"#;

which is asymptotically stable at its equilibrium,and its Jacobian is R ?

à6

à7

!.For simplicity,we assume that two connected nodes are coupled respectively by their corresponding state variables,

that is the inner-coupling matrix can be expressed as C ?10

01 !,and the outer con?guration matrix is chosen as

A ?à531100à431010à100010à211002à32666643

5,which is weighted and asymmetric.The eigenvalues of A are respectively,k 1=0,k 2=à1.0756,k 3=à4.8000+1.2118j,k 4=à4.8000à1.2118j and k 5=à4.3243,where j is the imaginary unit.The

coupling delay is assumed to be s =0.1.Hence,by Theorem 1,one can obtain the asymptotical stability of the synchronization manifold S for network (1),if the delayed equation (4)are asymptotically stable.By utilizing Matlab LMI Toolbox,we found that there exist two common positive-de?nite matrices P and Q such that the series

of LMIs (11)hold,where P 2?P 3?P 4?P 5?P ?0:145400000:133600000:145400000:133626643775and Q 2?Q 3?Q 4?Q 5?Q ?0:869400000:930700000:869400000:930726643

.It follows from Theorem 1that the synchronization manifold S is asymp-totically stable for any ?xed time delay.Fig.1shows the state variables x i 1(t )and x i 2(t )(i =1,2,3,4,5)of the coupled

network with the initial values randomly chosen from [à5,5].

1508J.Lu,D.W.C.Ho /Chaos,Solitons and Fractals 37(2008)1497–1510

J.Lu,D.W.C.Ho/Chaos,Solitons and Fractals37(2008)1497–15101509 6.Conclusion

Both local and global results are obtained for the synchronization of complex delayed dynamical network with asymmetric and reducible coupling matrix.Based on the geometrical decomposition of network’s states and Lyapu-nov–Kolmanovskii theorem,some su?cient delay-independent and delay-dependent criteria have been derived for the stability of the synchronization manifold S in this paper.The obtained LMI criteria can be performed e?ciently via existing numerical algorithms such as the interior-point algorithms by using Matlab Toolbox.Numerical simulation is also given to verify theoretical result.

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GMP管理文件原辅包装材料检验制度

GMP管理文件原辅包装材料检验制度一、目的：为规定原辅材料、包装材料实验的内容和管理要求，特制定本制度。二、适用范围：适用于药用原辅材料和包装材料的检验和管理工作。三、责任者：质量监督科负责人、生产管理部负责人、仓库保管员、QA人员。四、正文： 1 管理职能 1.1 凡生产用的各种原辅材料和包装材料进库前均应经过检验，不符合规定或影响产品质量的原辅包装材料不得进库和投入使用。 1.2 特殊情况需降级使用者，应由供销部门先填写原辅材料、包装材料降级使用申请单，报质量监督科审查，由主管厂长批准后，才能使用。 2 管理内容与要求 2.1 仓库填写请验单必须填清原料名称、送验目的、产地、编号、批号、数量、件数、送检日期、请验单位、送检人等规定的全部项目，化验员复核无误后，才能取样，并发给抽样证。送检单中的数量必须与进仓数量相符，且检验后不得更改。 2.2 质量监督科按有关取样管理制度进行取样并及时检验。 2.3 原辅材料、包装材料均按公司制订的制度检验入库，需配套使用的包装材料还应经第二次配套检验合格后才能使用。 2.4 不合格原辅材料、包装材料检验单，需盖上质量监督科专用章，作为财务部门拒付的依据。

物料管理标准文件物料管理标准文件条目一、物料采购管理规定注：第一标准文件都应有这样的格式文头。

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土耳其电力市场分析

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数据来源：EüA?，TE?A?，TEDA?。土耳其电力市场自由化时间表二、土耳其电力市场自由化时间表在土耳其电力工业的发展初期，曾有外国企业参与，之后由地方公共团体承担。1950年以后，私营企业逐渐参与。1970年10月，根据国家第1312号法令，设立土耳其电力局(TEK)，垄断性的经营发电、输电、配电业务。根据土耳其3096号法令，从1984年开始，允许私营部门进入电力市场，但只有极少数的民营企业参与经营电力。1994 年，一贯垄断经营发电、输电、配电的TEK被分割成发电、输电公司TEA?和配电公司TEDA?。2001年 TEA?解体为EüA?、TE?A?和TEDA?，这三家公司的主营业务分别是发电、输电和零售。2005-2010年，土耳其配电领域的私有化开始，预计在2005-2010的5年中TEDA?将被21个私营配电公司所取代。2007年，土耳其发电领域开始了私有化进程。2008年，拥有总装机容量141MW的ADüA?公司成功完成了私有化，这是土耳其政府私有化管理局（Privatisation Administration）

unit4globalwarming单词和句型重点总结

Unit 4 Global warming全球变暖一、词汇 about发生；造成注意：（1）come about是不及物动词短语，不能用于被动语态，常指情况不受人控制的突然发生。有时用it作形式主语，that从句作真正主语。（2）表示“发生”的词或短语有：happen,occur,take place,break ① Many a quarrel comes about through a misunderstanding. ② The moon came out from behind the clouds. ③ I’ll let you know if anything comes up. ④ I’ll come over and see how you are coming along. ⑤ I came across an old friend yesterday. ⑥ When she came to, she couldn’t recognize the surroundings. ① I subscribe to your suggestion. ② Which magazine do you subscribe to? ③ He subscribed his name to the paper（文件）. ④ He subscribed a large sum to the poor students. n.量；数量

① It’s cheaper to buy goods in quantity / in large quantities. ② A large quantity of silk is sold in Japan. ③ A large quantity of drugs are found in his home. ④ Large quantities of rain are needed in this area. ① He tends to get angry when others disagree with her. ② His views tend towards the extreme（极端）. ③ He was tending (to) his son when I saw him in the hospital. ④ Jane is nice but has a tendency to talk too much. =Jane is nice but she tends to talk too much. ① The price of the new house in our area has gone up by 1,000 yuan per square meter（平方米）。That is（也就是说）it has gone up to 5,000 yuan per square meter. ② The wind has gone down a little. ④ The country has gone through too many wars.

工业设计创新与工业设计教育发展

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中东国家有哪些风俗

中东包括那些国家？ “中东地区”或“中东”是指地中海东部与南部区域，从地中海东部到波斯湾的大片地区，“中东”地理上也是非洲东北部与欧亚大陆西南部的地区。中东名称的来源据说是：16－17世纪欧洲殖民者向东殖民时，把距离欧洲的地理位置按远近划分成了：近东，中东，远东。中东大部分为西亚，但与西亚的区别是：1.中东不包括阿富汗。2.中东包括非洲国家埃及。3.中东包括了土耳其的欧洲部分。中东是两洋三洲五海之地，其处在联系亚欧非三大洲，沟通大西洋和印度洋的枢纽地位。其三洲具体指亚欧非三大洲，五海具体指里海，黑海，地中海，红海，阿拉伯海。交通便利，海陆空的路线，可顺利运送石油到各国。 “中东”不属于正式的地理术语。一般说来包括巴林、埃及、伊朗、伊拉克(专题，图库)、以色列、约旦、科威特、黎巴嫩、阿曼、卡塔尔、沙特、叙利亚、阿联酋和也门，巴勒斯坦、马格里布国家(阿尔及利亚、利比亚、摩洛哥、突尼斯)以及苏丹、毛里塔尼亚和索马里，由于其历史文化原因一般认为属于中东国家，土耳其和塞浦路斯尽管地理上属于中东地区的一部分，但是他们自身认为属于欧洲；北边的阿富汗有时也与中东联系密切。政治概念上的中东问题系指阿拉伯国家（包括巴勒斯坦）与以色列之间的冲突问题，也称阿以冲突。中东问题是列强争夺的历史产物，也是世界上持续时间最长的地区热点问题，至今已半个多世纪。中东问题的核心是巴勒斯坦问题。中东包括那些国家？使用的语言？ “中东”概念究竟包括哪些国家和地区，国内外尚无定论，但一般泛指西亚，北非地区，约24个国家，1500余万平方公里，3.6亿人口。西亚国家包括沙特、伊朗、科威特、伊拉克、阿联酋、阿曼、卡塔尔、巴林、土耳其、以色列、巴勒斯坦、叙利亚、黎巴嫩、约旦、也门和塞浦路斯。北非包括：苏丹、埃及、利比亚、突尼斯、阿尔及利亚、摩洛哥、马德拉群岛、亚速尔群岛阿拉伯国家主要用阿拉伯语、库尔德语、土耳其语、波斯语，以色列主要用希伯来语. 中东包括北非的埃及和西亚各国中除了阿富汗以外的其他国家。主要使用阿拉伯语。中东地区都有什么语言?各自国家的母语都是什么? 中东地区国家包括巴林、埃及、伊朗、伊拉克、以色列、约旦、科威特、黎巴嫩、阿曼、卡塔尔、沙特、叙利亚、阿联酋和也门，巴勒斯坦、马格里布国家（阿尔及利亚、利比亚、摩洛哥、突尼斯）以及苏丹、毛里塔尼亚和索马里,这里面大多数阿拉伯国家的通用语言是阿拉伯语,以色列的通用语言是希伯来语,伊朗的通用语言是波斯语,土耳其和塞浦路斯虽然地理上属于中东地区,但他们一般认为属于欧洲，而阿富汗虽地理上不属中东地区，但与中东联系密切.此外,在这些国家还有大量的民族,比如说库尔德族、贝督因各部族，这些民族说本民族的语言。而苏丹等东非洲国家通用英语. 因信奉伊斯兰教，通用官方语言是阿拉伯语，只是类似于我国的方言，发音有区别，以色列说的是希伯来语，伊朗说的是波斯语，土耳其说土耳其语. 中东国家有哪些风俗? 阿联酋虽然是穆斯林国家，信仰伊斯兰教，但国家实行对外全方位开放，政策较开明，对外国人在衣食住行等方面没有太多的限制，超级市场可以买到猪肉及其制品，基本可满足居住在阿联酋各国人士的需求，值得注意的是：

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二、中线路线走向：中国（北京、郑州、西安、乌鲁木齐）——中亚——西亚及中东——中欧——西欧中亚一句话概况：（机遇）中亚地区电商起步晚，发展相对落后，算是一块未开垦的处女地。从相关资料了解到，目前，(优势)中亚大部分国家（包括哈萨克斯坦、乌兹别克斯坦、土库曼斯坦、吉尔吉斯斯坦、塔吉克斯坦和阿富汗斯坦）已经有宽带接入，网络基础设施建设有助于互联网用户的增长，但（劣势）中亚地区互联网的商业用途还远远低于亚洲其他国家。同时，由于物产相对匮乏，中亚地区居民生活所需品严重依赖进口，跨境电商是其目前主要的电商形式。根据市场调研来看，2015年中亚地区的跨境电商已有了重大改变，这主要得益于哈萨克斯坦进入了WTO提高了商业透明度、吉尔吉斯斯坦对欧盟消费进一步扩展等。而促进中亚地区电子商务迅速发展的原因主要有两点： 1、电子商务可以有效降低商品价差，同时由于信息不透明和贸易水平落后，市场上存在严重的价差，而中亚也成为了世界上货物最贵的地方。但是电子商务的发展和渗透可以有效地解决这一问题。 2、电子商务能够触及到传统进口市场无法满足的人群，包括女性（中亚地区居民多为穆斯林，女性有许多禁忌）、小企业和乡村企业。据悉，哈萨克斯坦的B2C网站chocolife.me和吉尔吉斯斯坦B2B网

站prodsklad.kg比较活跃，也在一定程度上刺激了中亚电商的发展。另外，由于（威胁）在中亚地区，信用卡使用限制，网络支付存在很大风险，货到付款是目前主要的支付方式。西亚及中东一句话概况：中东市场有两个鲜明的形象：（机会）一是易被忽视的“金矿”，二是跨境电商伺机爆发。从告了解到，中东地区电商市场从2011年的70亿美元增长至2012年的90亿美元，有29%的涨幅，2013年这一规模达到112亿美元，2014年达到128亿美元，2015年突破150亿美元。中东地区各国电商渗透率为：阿联酋46%，沙特阿拉伯25%，黎巴嫩9%，埃及8%，科威特35%。根据Research and Markets的报告，从B2C电商销售额来看，阿联酋是中东地区最大的B2C电商市场，沙特阿拉伯是中东地区第二大B2C电商市场。在电商基础设施上，物流方面，中东地区的公司只能通过公路传送货物而不是飞机，且目前没有公认的法律规定可参考。支付方面，大约80%的网上购物是货到付款，15%是信用卡和借记卡支付。由于联系亚、欧、非三大洲，沟通大西洋、印度洋，中东地区自古以来就凭借十分重要的地理位置成为国际贸易要塞。这一地区给人的总体感觉是，居民有钱（石油输出国），但物资缺乏，所以人们跨境网购的热情非常高。在这一背景下，Amazon、eBay等全球电商早早的就进入中东市场，而近年来，中国的电商企业在此也颇为活跃。根据中国跨境出口电商商

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《Unit 4 Global warming》 Does It Matter? 一、语法填空(根据课文内容、依据语法规则完成下面短文） When 1________ (compare) with most natural changes, that the temperature of the earth rose about one degree Fahrenheit during the 20th century is quite shocking. And it’s human activity 2________ has caused this global warming rather 3________ a random but natural phenomenon. Dr. Janice Foster explains that we add huge 4________ of extra carbon dioxide into the atmosphere by burning fossil 5________. From the second 6________ and the discovery of Charles Keeling, all scientists believe that the burning of more and more fossil fuels 7________ (result) in the increase in carbon dioxide. Greenhouse gases continue to build up. On the one hand, Dr. Foster thinks that the trend would be a 8________. On the other hand, George Hambley 9________ (state) that more carbon dioxide would encourage a greater range of animals and bring us 10________ better life.

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土耳其的经典谚语土耳其在中世纪曾一度是世界上最强大的国家之一，她的强大绝非偶然，而是和这个民族的血液与文化有关的，下面整理了土耳其谚语，欢迎大家阅读。土耳其谚语(热门)一小勺盐能调好一大碗汤犬吠，而驮队继续向前。与朋友吃喝，可是别跟他们做生意。邻人的鸡仔如鹅;邻人的妻子娇如娥。通红的果子招石头。上帝也给每只笨鸟儿准备了一个矮树枝。上帝每关上一扇门，就打开另外一千扇。如果技能可以看会的话，那么每条狗都能开肉铺了。 “说”是耕种，“听”才是收获。能力的话没有学校的。土耳其谚语(最新)长远来看，吝啬鬼和慷慨人花出去的还是一样多。饥饿的肚子是不长耳朵的。未至溪流前，莫把裤腿卷。每个“糟糕”背后还有个“更糟糕”。闲散如酸醋，会软化精神的钙质;勤奋如火酒，能燃烧起智慧的

火焰。科学的敌人，不比朋友少。不学习的人总以后悔而告终。真理不需要喋喋不休的誓言。不劳动的玩乐，就象没有放盐的面包。谎言的船开不远。土耳其谚语翻译İnsanoğlu bir varmış bir yokmuş, dünya gelip geçicidir. 人如匆匆过客，天地亦非永恒。 Hırsızlık bir ekmekten, kahpelik bir öpmekten. 盗物一次便是贼，卖淫一回即为娼。 Ağustosta gölge kovan, zemheride karnı ovar. 夏天干活不卖力，冬天就要饿肚皮。 Akı karası geçitte belli olur. (或者) Ak göt, kara göt geçit başında belli olur. 是骡子是马，拉出来遛遛。 Duvarı nem, insanı gam yıkar. 潮湿摧墙倒，忧伤催人老。

土耳其礼品及家用电器展览会展后分析报告

展会名称：第20届2009土耳其国际家庭用品、礼品及家用电器展览会 (Zuchex) 展览时间：2009年10月15日至18日展览地点：土耳其，伊斯坦布尔，TüYAP展览中心, 展馆名称：1号 --10号展馆网站：https://www.sodocs.net/doc/559556711.html, 展会综述：这届2009年秋季展，有超过1000间来自22个国家和地区的企业参展，展厅规模达到10个展厅之雄伟规模。该展是世界第四，欧洲第三的家庭用品展览会，是第20届举办。每年分春秋两届举行，展出面积达到 60，000平方米。2008年秋季展已经有16个国家和地区的550多家企业参展，专业买家超过45，000人次，来自全球100个国家和地区，主要来自欧洲、美国、中东及亚洲等地。土耳其每年官方消费品部分采购进口额为10亿欧元，近几年越来越多的西欧买家发现该展是个不错的产品采购资源，这部分买家的数量正呈显著增长的趋势。由于土耳其毗邻欧亚非三大陆的特殊地理环境，使该展成为辐射欧亚非三大陆的枢纽型展览会。2008年春季开始该展首次设立国际展区，是有意进军欧亚市场的出口型贸易和生产企业的绝佳良机。参展范围：家用小电器，各类礼品，家居装饰品，家纺用品，餐厨用品，玻璃制品，塑料制品，陶瓷制品，灯具及照明设备。买家分布：欧洲，南北美，亚洲，中东，非洲新产品推荐：

藤制家居用品 Portable Grill Standard Drum Oven 背景为画的tableware 花纹典雅高尚的Dinnerware

展会情况及市场展望：开展4天，我司展位一直是同列展位买家人流最旺，受关注度最高之处.虽然同行https://www.sodocs.net/doc/559556711.html,紧靠旁边，他们非常羡慕我司展位前驻足登记询盘的买家数量之多，并表示他们参该展数次，第一次见有如此的买家人流量。这次来我司登记的买家多数为各公司的President或者Import Manager,占买家比率77.83%，其余问贸易公司和采购商的Product Develop Manager。在历史过程中，作为连接亚欧大陆的灵魂之都，伊斯坦布尔成为丝绸之路之间的东部和西部的世界过渡点，至今仍保持这一传统的生存延续。该枢纽型展览会的举办，吸引了不少来自欧洲，中东，亚洲，非洲和南北美洲的买家，对2010年这些地区的家居和家电用品发展趋势起了至关重要的作用。环球市场展会专业展会数据分析

在中东做生意

如何在中东做生意 2010-05-11 11:10:39| 分类：关于中东.中国商阅读376 评论0 字号：大中小订阅 -- 关于中东市场中东指巴林、塞浦路斯、埃及、伊朗、伊拉克、以色列、约旦、科威特、黎巴嫩、阿曼、卡塔尔、沙特阿拉伯、叙利亚、阿联酋、也门等 15 个国家。一、市场概述中东市场通常指环绕波斯湾和阿拉海的9个国家和周边阿拉伯国家，总人口达到5-7亿，人均年收入从阿联酋，科威特等的3-4万美元到伊朗，伊拉克，也门等国家的年人均收入5-6千美元不等，这些阿拉伯国家的轻工，日用，电子，服装基本外要依赖进口，产品的价格要求为中低要求，档次不是非常高.同时这些部分地区，几乎可以讲是一种完全纯消费的特点。中国产品在全世界以物美价廉著称，中国作为世界第一轻工，电器，服装等产品大国，以绝对优势占据整个中东市场。尽管欧美市场是目前世界上最发达、最成熟的市场，但这个市场的竞争十分激烈，商品趋于饱和，加上高进口关税及贸易壁垒的限制，后来者或中小实力的企业很难进入。纵览当今世界，唯有中东和非洲市场是一个充满商机、前景良好的热点市场。说起中东，就不能不提阿联酋和迪拜。迪拜是阿联酋7个酋长国中的一个，位于阿拉伯半岛的东端，处于"五海三洲"中点的重要战略位置，是东西方的交通要道和贸易枢纽。每天通过迪拜转口的集装箱达到几万个，为中东第一大港口，在迪拜你可以找到全世界120国家的商人，他们常年穿梭于中东与本国，从事商品贸易。据不完全统计，阿联酋年贸易额约800亿美元，由于自然资源的匮乏，除了石油和天然气外的其它产品，从工业用原料、设备到民用生活物品均依赖进口，故阿政府一直实行开放的自由贸易政策，没有贸易壁垒，无外汇管制及其管理机构，从得到授权的银行可以无限制地获得外汇，没有征收公司或企业的利润税和营业税的规定，没有所得税、增值税、消费税和中间环节的各种税收，利润可以自由汇出。除烟、酒等极个别商品外，其它大部分商品只是象征性征收1%-4%的关税。外贸在阿联酋经济中占有重要位置。阿各类商贸公司14108家，其中外国公司680家，国有中国公司37家，自由贸易区4个。1995年，加入世界贸易组织。进口主要有粮食、机械和消费品。阿转口贸易比重较大，同100多个国家和地区有贸易关系，与40多个国家签订了双边贸易协议和避免双重征税协议。我国主要出口阿联酋的主要产品为：轻工，纺织，机电，和家用电器，由于国内厂家对阿市场的重视不够，使得出口产品的质量有所下降，直接影响到价格，目前所有出口产品的纯利润从1997年的45%，下降到17%，部分产品下降到10%左右，在2001年出口中东，仅仅到迪拜港口的货物容值达到25亿美元。往来中东80%以上的货物要经过迪拜进行中转，同时辐射到非洲大部分国家，辐射人口达到13亿。在这里云集了非洲近30多个国家的客商，常年在这里采购日用，轻工，电器，服装，等货物。通常进口交易额度的75%转口非洲市场，20%转口周边海湾国家，5%直接在阿联酋消费。迪拜素有“中东的香港”之美誉，是阿联酋的金融经济中心，以其自由宽松的经济政策、得天独厚的地理位置、完善齐备的基础设施，迅速成为中东地区的交通枢纽和最大的货物集散地。通过迪拜，货物可转销到海湾地区、俄罗斯、东欧、非洲、地中海。目前我国产品以种类繁多、档次适中、规格齐全、价格合理颇受青睐，进一步开发潜力极大，尤其是机电五金、汽摩配件、纺织服装、轻工工艺极具竞争优势。通过迪拜，货物可转销到海湾地区、东欧、非洲、南亚。海湾地区以盛产石油天然气闻名于世界，石油天然气的储量占世界65%以上，沙漠面积占陆地面积80%以上。整个海湾地区除了石油天然气工业比较发达以外，几乎没有其它的工业。全部的工业产品依赖进口。

原材料分类

材料分类明细一、原材料（一）、主要材料 1、主材--水泥 2、主材--钢材 3、主材--地材 4、主材--钢铰线 5、主材--炸材（代号品） 6、主材--木材 7、主材--水泥制品 8、主材--沥青 9、其他主材（二）、辅助材料包含粉煤灰、外加剂、连接套筒、锚具、声测管、竹胶板、橡胶支座、土工材料、塑料排水管等。（三）、机械配件（四）、油料 1、油料--燃油 2、油料--润滑油二、周转材料包含各类模板、架管、扣件、型材、贝雷架、轨道、活动房等可以重复利用的材料。三、低值易耗品不包含在以上各类材料中的其它材料及各类小型设备。

原材料科技名词定义中文名称：原材料英文名称：raw material 定义：投入生产过程以制造新产品的物质。应用学科：机械工程（一级学科）；机械工程(2)总论（二级学科）以上内容由全国科学技术名词审定委员会审定公布求助编辑百科名片原材料原材料即原料和材料。原料(raw material)一般指来自矿业和农业、林业、牧业、渔业的产品；材料(processed material)一般指经过一些加工的原料。举例来讲，林业生产的原木属于原料，将原木加工为木板，就变成了材料。但实际生活和生产中对原料和材料的划分不一定清晰，所以一般用原材料一词来统称。目录简介种类入账处理展开简介种类入账处理展开编辑本段简介原材料即原料和材料。原料(raw material)一般指来自矿业和农业、林业、牧业、渔业的产品；材料(processed material)一般指经过一些加工的原料。原材料在会计中的定义是：原材料是指经过加工能构成产品主要实体的各种原料、材料及不构成产品主要实体但有助于产品形成的各种辅助材料。原材料是企业存货的重要组成部分，其品种、规格较多，为加强对原材料的管理和核算，需要对其进行科学的分类。举例来讲，林业生产的原木属于原料，将原木加工为木板，就变成了材料。但实际生活和生产中对原料和材料的划分不一定清晰，所以一般用原材料一词来统称。

土耳其概况

土耳其概况【国名】土耳其共和国（Republic of Turkey）。【面积】78.36万平方公里，其中97%位于亚洲的小亚细亚半岛，3%位于欧洲的巴尔干半岛。【人口】7256万，土耳其族占80%以上，库尔德族约占15%；城市人口为4970多万，占总人口的70.5%。土耳其语为国语。99%的居民信奉伊斯兰教，其中85%属逊尼派，其余为什叶派（阿拉维派）；少数人信仰基督教和犹太教。【首都】安卡拉（Ankara），人口447万，年最高气温31℃，最低气温－4℃。【政体】共和制【货币】土耳其里拉（Turkish Lira）。【国家元首】总统阿卜杜拉·居尔（Abdullah Gül）, 2007年8月28日由议会选出，当日就任。【主要节日】新年：1月1日；国家主权和儿童日：4月23日；青年和体育节：5月19日；胜利日：8月30日；共和国成立日：10月29日。【简况】地跨亚、欧两洲，邻格鲁吉亚、亚美尼亚、阿塞拜疆、伊朗、伊拉克、叙利亚、希腊和保加利亚，濒地中海、爱琴海、马尔马拉海和黑海。海岸线长7200公里，陆地边境线长2648公里。南部沿海地区属亚热带地中海式气候，内陆为大陆型气候。

土耳其人史称突厥，8世纪起由阿尔泰山一带迁入小亚细亚，13世纪末建立奥斯曼帝国，16世纪达到鼎盛期，20世纪初沦为英、法、德等国的半殖民地。1919年，凯末尔领导民族解放战争反抗侵略并取得胜利，1923年10月29日建立土耳其共和国，凯末尔当选首任总统。【政治】2002年11月，正义与发展党在土第22届议会选举中获胜，实现单独执政，结束了土自1987年以来多党联合执政的局面。正义与发展党上台后，积极推进政治、经济改革，统筹社会协调发展，取得明显成效。2007年7月，正发党以46.6%的得票率赢得大选，继续单独执政。 2011年6月，土举行第24届议会选举，正发党以49.9%的得票率赢得胜利，实现第三次连续单独执政。【宪法】土立法体系效仿欧洲模式。现行宪法于1982年11月7日生效，是土第3部宪法。宪法规定：土为民族、民主、政教分离和实行法制的国家。【议会】全称为土耳其大国民议会，是土最高立法机构。共设550个议席，议员根据各省人口比例经选举产生，任期4年。实行普遍直接选举制，18岁以上公民享有选举权。只有超过全国选票10%的政党才可拥有议会席位。本届议会成立于2011年6月29日，是土第24届议会。目前议会议席分布情况是：正义与发展党327席，共和人民党135席，民族行动党52席，和平民主党29席，无党派7席。【政府】又称部长会议。本届政府是土第61届政府，成立于2011年7月13日，系正义与发展党单独执政，法定任期4年。【行政区划】土耳其行政区划等级为省、县、乡、村。全国共分为

Global warming全球变暖全英文介绍

One of the effects of global warming is the destruction of many important ecosystems.Changing and erratic climate conditions will put our ecosystems to the test, the increase in carbon dioxide will increase the problem. The evidence is clear that global warming and climate change affects physical and biological systems. There will be effects to land, water, and life. Already today, scientists are seeing the effects of global warming on coral reefs, many have been bleached and have died. This is due to warmer ocean waters, and to the fact that some species of plants and animals are simply migrating to better suited geographical regions where water temperatures are more suitable. Melting ice sheets are also making some animals migrate to better regions. This effects the ecosystems in which these plants and animals live. Several climate models have been made and they predict more floods (big floods), drought, wildfires, ocean acidification, and the eventual collapse of many ecosystems throughout the world both on land and at sea. There have been forecasts of things like famine, war, and social unrest, in our days ahead. These are the types of effects global warming could have on our planet. Another important effect that global warming will bring is the loss and endangerment of many species. Did you know that 30 percent of all plant and animal species alive in the world today are at risk of extinction by the year 2050 if average temperatures rise more than 2 to 11.5 degrees Fahrenheit. These mass extinctions will be due to a loss of habitat through desertification, deforestation, and ocean warming. Many plants and animals will also be affected by the inability to adapt to our climate warming.

工业设计创意方案

一.网格式晾衣竿 1.创意摘要：网格式晾衣竿 2.拟解决得问题：晾衣空间不足（寝室）,只有一根晾衣竿 3.解决方案：将晾衣竿改造成网格式，增加晾衣空间，且可随太阳方向调节衣物朝向 4.附图：二.升降式晾衣竿 1.创意摘要:晾衣竿可随拉线上升或下降 2.拟解决得问题：老人抬手不方便，不便使用撑衣叉 3.解决方案：利用卷帘得原理使晾衣竿可随拉线上升或下降

4 . 伸缩式晾衣竿 1.创意摘要：晾衣竿可延伸出阳台外 2.拟解决得问题：公寓及一般套房低矮阴凉，即使有太阳也不易晾干 3.解决方案：利用拉门，雨棚两边四边形结构得可变性能构造出可延伸式晾衣竿

单边圉，未画晾衣竿 4.附图：四.可拔取式台灯 1.创意摘要:台灯与手电筒合二为一 2.拟解决得问题：突然停电时，无法立刻拿到手电筒 3.解决方案：停电时，由于灯有储存电力得功能，不会立刻灭灯，也可以将灯并从台灯底拔出来，随人任意走动 4.附图: 五.可变形椅 1.创意摘要:寝室内椅子可由单人靠背椅变形为双人无背凳 2.拟解决得问题：同学，朋友或家长来时无座位可坐 3.解决方案：将椅子得椅背改造成可翻折式样，另外附加两根可扭转式得凳子腿

Kt 加椅AS 僂1面團 4.附图：六.可移动式书架隔板 1. 创意摘要:书架隔板可随书本得高度调节 2. 拟解决得问题：书架固定不变时，有些书太高无法竖立直放 3. 解决方案：利用老式躺椅调节椅背倾斜度得原理，以及三角形得稳固性创意方案一《奇妙得鞋子》4.附图: 椅子背面图

一、创意摘要或多或少有点路痴基因得朋友，您们一定理解拐过两个路口就找不北得痛苦。也许百度谷歌地图可以帮您寻找，但还要一步一步得寻找，有些地方您也根本不熟悉，这样就比较麻烦，那么, 怎么样比较好得解决这个问题呢？这就是这款“神奇得鞋子”可以帮助您解决疑惑。二、解决得问题帮助方向感较差，或者对某一个地方不熟悉得时候，辨清方向。三、建议解决得方案在鞋子脚跟部位有一个GPS设备与天线,在鞋头还有两套LED方位指示灯，右鞋得灯就是用来告知您距目得地还有多远,左鞋则就是告知您正确得方向。当然了,在使用前,得用USB连接鞋并在专用得地图软件上设置您得目得地，需要时，点击一下鞋跟部位，就可以启用了。四、附件创意方案二《旧物改造》一、创意摘要生活当中，我们总就是喜欢喝各种各样得饮料，而我们在选择得时候，不仅仅就是因为饮料得味道，还有一部分原因就是因为饮料瓶子好瞧。喝完之后，再好瞧得饮料瓶子也没有什么用武之地了，这样就会很可惜。为了让它能够再次发挥价值，我们可以稍稍得把饮料瓶子改造一下就可以了。二、解决得问题旧物重新利用，把饮料瓶制成零钱包。三、建议解决得方案事实上,就是非常简单得，我们取下两个塑料瓶得底部，在用一条拉链将她们缝制在一起可以根据自己得喜欢，调制高度。一个好瞧得零钱包就可以制成了。

globalwarming教案

Teaching Plan Contents: Reading Book 6 Unit 4 Global warming I.Analysis of the Teaching Material This article is from a magazine about global warming, which illustrates how global warming has come about and different attitudes to its effects. The passage is long, abstract and far away from their life. What’s more, there are many mouthful professional terms, which increases students’ difficulty while reading, although they have some knowledge about global warming. II. Analysis of the Students Students from Senior Two are the students in an excellent level, who have good abilities to read and speak. This unit talks about global warming, which has been taught in Geography. It will help students understand the text better and I believe the students will be interested in this class. However,because they pay little attention to this topic in the daily life, they may have few desire to speak something about global warming. III. Teaching objectives 1. Knowledge objective 1) Enable the students to analyze how global warming has come about； 2) Get students know different attitudes towards global warming and its effects. 2. Competence objective Improve the students’ reading and speaking abilities. 3. Emotion objective 1) Develop student s’ teamwork. 2) Raise their awareness of global warming. IV. Important points Enable the students to understand how global warming has come about. V. D ifficult points Get the students understand how global warming has come about. Let the students understand the difficult sentences better. ①It is human activity that has caused this global warming rather than a random but natural phenomenon. (Line 6) ②All scientists subscribe to the view that the increase in the earth’s temperature is due t o the burning of fossil fuels like coal, natural gas and oil to produce energy. (Line 18) ③This is when small amounts of gases in the atmosphere, like carbon dioxide, methane and water vapour, trap heat from the sun and therefore warm the earth.(Line 26-29) VI. Teaching aids: Multimedia classroom, printed material VII. Teaching methods: Task-based teaching, communicative teaching method VIII.Teaching procedures: Step 1. Lead in and pre-reading (5 mins ) It’s reported that global temperatures continue to rise, making July 2016 the hottest month in the history of the earth. Did you feel extremely hot in July? When you felt hot, what did you do? Did you feel global temperatures going up quietly? Let’s look at a flash (global temperatures from 1850 to 2016). What information can you get? The earth is becoming warmer and warmer. Is it natural or caused by human being? Do you think what effects global warming will bring about? Is global warming beneficial or harmful? Today we’re going to read a magazine article about global warming. It will work out your puzzles. Please open your book and turn to P26. Today we are going to

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