Synchronization of spatiotemporal chaos in complex networks via backstepping

doi:10.1088/1674-1056/21/3/030506

Abstract A backstepping approach is proposed for the synchronization of chain networks of multi-spatiotemporal chaotic systems with topologically equivalent structures. The synchronization of multi-spatiotemporal chaotic systems is implemented by adding the control only to a terminal node, and the controller is designed via a corresponding update law. The control law is applied to spatiotemporal Gray-Scott systems. Numerical results demonstrate the effectiveness and the feasibility of the proposed approach.

Keywords: spatiotemporal chaos backstepping design Lyapunov function chain complex networks

Received: 12 July 2011
Revised: 09 October 2011
Accepted manuscript online:

PACS:	05.45.Xt	(Synchronization; coupled oscillators)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: Project supported by the National Outstanding Young Scientists Foundation of China (Grant No. 10725209), the National Natural Science Foundation of China (Grant Nos. 90816001 and 10902064), the Shanghai Subject Chief Scientist Project, China (Grant No. 09XD1401700), the Shanghai Leading Talent Program and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106), the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT0844), the Natural Science Foundation of Liaoning Province, China (Grant No. 20082147), and the Innovative Team Program of Liaoning Educational Committee, China (Grant No. 2008T108).

Corresponding Authors: Chen Li-Qun,lqchen@staff.shu.edu.cn
E-mail: lqchen@staff.shu.edu.cn

Cite this article:

Chai Yuan(柴元), LŰ Ling(吕翎), and Chen Li-Qun(陈立群) Synchronization of spatiotemporal chaos in complex networks via backstepping 2012 Chin. Phys. B 21 030506

[1]	Ott E, Grebogi C and Yorke J A 1990 Phys. Rev. Lett. 64 1196
[2]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[3]	Guo R W 2008 Phys. Lett. A 372 5593
[4]	Yang T, Yang C M and Yang L B 1997 Phys. Lett. A 232 356
[5]	Nazzal J M and Natsheh A N 2007 Chaos Soliton. Fract. 33 695
[6]	Chen L Q 2004 Chaos Soliton. Fract. 21 113
[7]	Chen L Q 2001 Phys. Lett. A 281 327
[8]	Mascolo S and Grassi G 1997 Phys. Rev. E 56 6166
[9]	Njah A N, Ojo K S, Adebayo G A and Obawole A O 2010 Physica C 470 558
[10]	Laoye J A, Vincent U E and Kareem S O 2009 Chaos Soliton. Fract. 39 356
[11]	Sharma B B and Kar I N 2009 Chaos Soliton. Fract. 41 2437
[12]	Pishkenari H N, Jalili N, Mahboobi S H, Alasty A and Meghdari A 2010 Chaos 20 023105
[13]	Yu Y G and Li H X 2011 Nonlinear Anal. Real World Appl. 12 388
[14]	Watts D J and Strogatz S H 1998 Nature 393 440
[15]	Newman M E J and Watts D J 1999 Phys. Lett. A 263 341
[16]	Barab醩i A and Albert R 1999 Science 286 509
[17]	Liu H, Song Y R, Fan C X and Jiang G P 2010 Chin. Phys. B 19 070508
[18]	Hu A H, Xu Z Y and Guo L X 2011 Chin. Phys. B 20 090511
[19]	Silva J A L, Barrionuevo J A and Giordani F T 2010 Nonlinear Anal. Real World Appl. 11 1005
[20]	Ahn C K 2010 Nonlinear Dyn. 60 295
[21]	Sorrentino F and Ott E 2008 Phys. Rev. Lett. 100 114101
[22]	Gorochowski T E, Bernardo M D and Grierson C S 2010 Phys. Rev. E 81 056212
[23]	Flunkert V, Yanchuk S, Dahms T and Sch髄l E 2010 Phys. Rev. Lett. 105 254101
[24]	Chen W S, Li W and Miao Q G 2010 ISA Trans. 49 283
[25]	Lin D, Wang X Y, Nian F Z and Zhang Y L 2010 Neurocomputing 73 2873
[26]	Grigoriev R O, Cross M C and Schuster H G 1997 Phys. Rev. Lett. 79 2795
[27]	Zhang Q L, L? L and Zhang Y 2011 Chin. Phys. B 20 090514
[28]	Parekh N, Parthasarathy S and Sinha S 1998 Phys. Rev. Lett. 81 1401
[29]	Wang X F and Chen G R 2002 Physica A 310 521
[30]	Li X, Wang X F and Chen G R 2004 IEEE Trans. Circ. Syst. I 51 2074
[31]	Chen T P, Liu X W and Lu W L 2007 IEEE Trans. Circ. Syst. I 54 1317
[32]	Pearson J E 1993 Science 261 189
[33]	L? L, Chai Y and Luan L 2010 Chin. Phys. B 19 080506

[1]	An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree Yining Su(苏怡宁), Xingyuan Wang(王兴元), and Shujuan Lin(林淑娟). Chin. Phys. B, 2022, 31(11): 110503.
[2]	A novel pseudo-random coupled LP spatiotemporal chaos and its application in image encryption Xingyuan Wang(王兴元), Yu Wang(王宇), Siwei Wang(王思伟), Yingqian Zhang(张盈谦), Xiangjun Wu(武相军). Chin. Phys. B, 2018, 27(11): 110502.
[3]	Stability analysis of a simple rheonomic nonholonomic constrained system Chang Liu(刘畅), Shi-Xing Liu(刘世兴), Feng-Xing Mei(梅凤翔). Chin. Phys. B, 2016, 25(12): 124501.
[4]	Two kinds of generalized gradient representationsfor holonomic mechanical systems Feng-Xiang Mei(梅凤翔) and Hui-Bin Wu(吴惠彬). Chin. Phys. B, 2016, 25(1): 014502.
[5]	Secure communication based on spatiotemporal chaos Ren Hai-Peng (任海鹏), Bai Chao (白超). Chin. Phys. B, 2015, 24(8): 080503.
[6]	Skew-gradient representation of generalized Birkhoffian system Mei Feng-Xiang (梅凤翔), Wu Hui-Bin (吴惠彬). Chin. Phys. B, 2015, 24(10): 104502.
[7]	Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with discrete and distributed time varying delays M. Syed Ali. Chin. Phys. B, 2014, 23(6): 060702.
[8]	Lyapunov function as potential function：A dynamical equivalence Yuan Ruo-Shi (袁若石), Ma Yi-An (马易安), Yuan Bo (苑波), Ao Ping (敖平). Chin. Phys. B, 2014, 23(1): 010505.
[9]	A self-adapting image encryption algorithm based on spatiotemporal chaos and ergodic matrix Luo Yu-Ling (罗玉玲), Du Ming-Hui (杜明辉). Chin. Phys. B, 2013, 22(8): 080503.
[10]	Global dynamics of a novel multi-group model for computer worms Gong Yong-Wang (巩永旺), Song Yu-Rong (宋玉蓉), Jiang Guo-Ping (蒋国平). Chin. Phys. B, 2013, 22(4): 040204.
[11]	Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters Li Fan (李凡), Wang Chun-Ni (王春妮), Ma Jun (马军). Chin. Phys. B, 2013, 22(10): 100502.
[12]	Cryptanalysis on an image block encryption algorithm based on spatiotemporal chaos Wang Xing-Yuan(王兴元) and He Guo-Xiang(何国祥) . Chin. Phys. B, 2012, 21(6): 060502.
[13]	One-way hash function construction based on the spatiotemporal chaotic system Luo Yu-Ling(罗玉玲) and Du Ming-Hui(杜明辉) . Chin. Phys. B, 2012, 21(6): 060503.
[14]	The signal synchronization transmission of a spatiotemporal chaos network constituted by a laser phase-conjugate wave Li Wen-Lin(李文琳), Li Shu-Feng(李淑凤), and Li Gang(李钢) . Chin. Phys. B, 2012, 21(6): 064217.
[15]	Stability analysis of nonlinear Roesser-type two-dimensional systems via homogenous polynomial technique Zhang Tie-Yan (张铁岩), Zhao Yan (赵琰), Xie Xiang-Peng (解相朋). Chin. Phys. B, 2012, 21(12): 120503.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Synchronization of spatiotemporal chaos in complex networks via backstepping

Cite this article:

Online attention