驱动和响应混沌同步

【实例简介】
利用非对称非线性函数耦合混沌同步方法, 讨论了Chen 吸引子的混沌同步问题, 数值模拟分析初始值和耦合强度因子的选择对于实现混沌同步的影响.
4714 57 60 20 40 20 0 20 0 x1 N 0 1 Chen ,(b) ,(c)y1-z1 (6) A (x1,y1,z1)=F1(X1(t) μ=5. (入=-27.45,入= 1(x2,y2,z2)=F2(X2(t)), 3. (5) OD1+1 (c-a)x1-x1z1+∞n|+a[(u-c)y1+x1z1-[(u-c)y2+x21 x1y1-bz 1 xiyi t a2 y2 an 2t a) 0 2=(c-a)x2-x2+cy2|+l(u-c)y2+x21-[(-)y1+x121 (10) 2 bz 2 y2+ x1r e2=x1(2)-x2(2)=-3,c3=x1(3)-x2(3)=0,e4 =x1(4)-x2(4)=-2 B=0.5 a=βa≠B o1994-2012ChinaAcademicJournalelEctronicPublishingHouse.Allrightsreservedhttp://www.cnki.net len 4715 1 (a=B=0.5 0.0 x1,x2 4,5 20,21 4.8 0.1 4.4 30,21 4,6 6.8 30.40 0. a=B=0.5 a+ 4.0 0.2 1(a+B=1) a+ a 0.0 0.5 1.0 (7),a+B=1,e(t)=Ae,e(t 0.2 ββ 1.5 -…--a=B=2.0 X1(1)X2(t (a+B=1) 0.1 09 0.3 0.5 3.完全连接-Chen吸引子网络的同步 0.7 03 0.9 en 01994-2012,2n314.cademicJournaleLectronicPublishinghOuse.Allrights'reserved.http://www.cnki.net 4716 57 (1)=AX(1)-D(X(1)) +an∑GD(X(1)).(11) G C}, ∑G;=0.D(X) 40 x ),Gi=N-1. X;-X, (i=1,2,…N-1) +1 dD (b) e(1)=14(Na-)xe 120:八 01=lN, ei t 80 X:(t)X+1() (12 X( t) Xi+j (t (12) L apunov 12 yapunov al=1N vapunov 4.星形子网络构成大网络的同步 4 Chen N 4.A D a l/4=0.25 a. b Runge kutta 5(a) x2,x1-33,x1-x4 21,22,233,24 21,22,23,24 (11 G 0 0 01 o1994-2012ChinaAcademicJournalelEctronicPublishingHouse.Allrightsreservedhttp://www.cnki.net len 4717 X1,X2,X1,X2 (Xx1,X2,x1),(X2,x2,X2 X=AXi-D(X)+star 3D(XD-D(X: A D(X)-D(X)] +aal D(Xi-D(Xil X=AX:-D(X )+ Bsta[-D(X) DCX =Ax-D(X)+B--D(X)+D(x2)], X:=AX:-D()+Ba[-DX)+ D(X) 2.i+1=1. 5,y1=1,z1=5;x1=-5.2,y1=1.3,x1=4.8; 12=-5.4,y12=0.7,zn=5.2;x13=-4.7, 4,z13=4.6 X-X1+ 4,y2=2, 10: i+1(i+2.3,…,N-1) 4.2,y21=2.1,z2=9.7;x=-4.4,y22-2.3,z2 =9.5;x=-3.7,y23=1.8,x23=10.2. 0.0,B4=1.0, 0. A+( aX 0.5 Runge- Kutta A (13 7( X2= X A+(N-1)ar+B4m-1) a4a=0.0.Bar=1.0,e1 am=0.0 CI )(x1,y1,x1) 11 aall M=2.N=3 unov an∈[0.25,0.70 apunov >0 70 994-2012'chinaAcademicJournalElectronicPublishingHouseAllrightsreservedhttp://www.cnki.net 4718 57 2 1=x1-X e2=x1-X12 e3=x1-x13 0.2 0. 0.6 L Lyapuov βr∈[0.49 12.43] Btm<0.49 2 e3=y2- 123 ,Ban>12.43 0 a1=0.5 0 punon ∈[ 0.181 astar astar 0.03,aad 0.0 atar?= 0 0.01 10 40 10 as ter= astar 20 2=-0.03 astar=astar=-0 01 0 0 z astar= astar=0. aa=0. 5 10 a o1994-2012ChinaacAdemicJournaleLectronicPublishingHouse.Allrightsreservedhttp://www.cnki.net len 4719 结论 Che nen [1 Pecora L M, Caroll T L 1990 Phys. Ret. Lett. 64 821 10 Udaltsov Vs, Goedgebuer J P, Larger L, Rhodes W T 2001 Phys [2] Yu H, Li Y Z2003 Phys. Lett. A 314 292 Rev. lett. 91892 [3 Yu H J, Peng J H 200.5 Acta Biophys. Sin. 21 295( in Chinese [11 Chen G, UetaT1999 Int. J. Bifur.Chaos 91465 2005 21295] 12] Ali M K, Fang JQ 1997 Phys. Re. E55 5285 [4] Yu HJ, Peng JH, Liu Y Z 2006 Int. Bif ur. Chaos 16 1049 13 Cheng Y X, Wang G R 1995 Acta Phys. Sin. 44 1382( in [5 Wu X J, Wang X Y 2006 Acta Phys. Sin. 55 6261[ Chinese) 1995 441382] 2006 5562611 [14 Yu H J, Liu Y Z 2005 Acta Phys. Sin. 54 3029( in Chinese[ [6] Agiza H N, Yassen M T 2001 Phys. Let. A 191 2005 43029] [71 Dhamala M, Jirsa V K, D ing M 2004 Phys. Rev. Lett. 92074104 15] Qin J, Yu H J 2007 Ad a Phys. Sin. 56 50( in Chinese)[ 8] Cuomo K M, Oppenheim A V 1993 Phys. Rev. Lett. 71 65 5650 [91 Kocarev L, Parl iz U 1995 Phys. Re. Lett. 74 5028 o1994-2012ChinaAcademicJournalelEctronicPublishingHouse.Allrightsreservedhttp://www.cnki.net 4720 57 Chaotic synchronization of network of Chen s chaotic attractors using nonlinear coupling function u Hong- Jie Zhe ng ning Dep atment f Engineering Mechanics, Shanghai Jiaotong Chiers it, Shanghai 200240, Chi ra) Received 13 O cober 2007; rev ied manuscript received 12 M arch 2008) abstract This article offers a method to realize the synchronization of non symmetrically nonlinear- coupled chaotic systems, studies the chaot ic synchronization of Chen's chaotic attra ctors, and analyzes the influence of chaotic synchronization by numerical simulation under different coupling strengths and different initial conditions. We also extend the synchronization method of nor symmetrically nonlinear coupled sy stems to the study of large network linked by numerous Chen s attractor sy stem units by afte alf- coupling and star coupling. We deduced the equation of errors which ensures the stability of synchronous state, studied the influence of different coupling strengths on sy nchronization stability and detem ined the range of coupling strengths which ensures the synchronizat ion. By numerical simulation we proved that if we choose nonlinear functions as coupling fundions, it effectively realizes the synchronization of alfter a H coupl ing network and large network linked from star sub networks. We can foresee that the noH symmetrically non linear coupled synchro nization method could be widely used in network sy nchronization Keywords: nonlinear coupling function, Chen's attractor, chaotic synchronization, networks PACC: 0545 sk Projed support ed by the National Natural Sc ence Foundation of China(Grant No. 1(672086)and the Docto ral Program Foundation of Inst itut on of Highe Educat in of China( Grant No. 20060248031) 1994-2012ChinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.cnki.net 【实例截图】
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