Hybrid Synchronization of Three Identical Coupled Chaotic Systems Using the Direct Design Method

Abstract:

This paper investigates the hybrid synchronization behavior (coexistence of anti-synchronization and complete synchronization) in three coupled chaotic systems with ring connections. We employ the direct design method to design the hybird synchronization controllers, which transform the error system into a nonlinear system with a special antisymmetric structure. A simple stability criterion is then derived for reaching hybrid synchronization. Finally, numerical example is provided to demonstrate the effectiveness of the theoretical analysis.

• Periodical: Advanced Materials Research (Volumes 912-914)
• Pages: 695-699
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.912-914.695
• Online since: April 2014
• Authors: Xiu Huan Ji*
• Keywords: Anti-Synchronization, Chaotic System, Complete Synchronization, Hybrid Synchronization Behavior, Ring Connection

References

[1] L. M. Pecora, T. L. Carroll. Synchronization in chaotic systems. Physical Review letters, 1990, 64(8): 821-4.

[2] B. Nana, P. Woafo, Domngang S. Chaotic synchronization with experimental application to secure communications. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(5): 2266-2276.

DOI: 10.1016/j.cnsns.2008.06.028

[3] P. Li, R. Dong, B. Lu. Hybrid Synchronization of Lv Hyperchaotic System with Disturbances by Sliding Mode Control. Procedia Engineering, 2011, 15(8): 23-27.

DOI: 10.1016/j.proeng.2011.08.006

[4] X. Chen, J. Qiu. Synchronization of N different chaotic systems based on antisymmetric structure, Mathematical Problems in Engineering, 2013, Article ID 742765, 6 pages.

[5] X. Chen, J. Qiu, Q. Song, A. Zhang. Synchronization of N coupled chaotic systems with ring connection based on special antisymmetric structure, Abstract and Applied Analysis, 2013, Article ID 680604, 10 pages.

DOI: 10.1155/2013/680604

[6] W. He and J. Cao, Global synchronization in arrays of coupled networks with one single time-varying delay coupling. Physics Letters A, 2009, 373(31): 2682-2694.

DOI: 10.1016/j.physleta.2009.05.041

[7] J. Cao, Z. Wang, and Y. Sun. Synchronization in an array of linearly stochastically coupled networks with time delays. Physica A, 2007, 385(2): 718-728.

DOI: 10.1016/j.physa.2007.06.043

[8] Y. Liu, L. Lv. Synchronization of N different coupled chaotic systems with ring and chain connections. Applied Mathematics and Mechanics, 2008, 29(10): 1181-1190.

DOI: 10.1007/s10483-008-1005-y

[9] G. Grassi. Propagation of projective synchronization in a series connection of chaotic systems. Journal of the Franklin Institute, 2010, 347(2): 438-451.

DOI: 10.1016/j.jfranklin.2009.10.004

[10] X. Chen, C. Wang, J. Qiu. Synchronization and anti-synchronization of N different coupled chaotic systems with ring connection. International Journal of Modern Physics C, Vol. 25, No. 4, 12 pages. (2014).

DOI: 10.1142/s0129183114400117