Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

doi:10.1088/1674-1056/22/10/100502

Abstract Complete synchronization could be reached between some chaotic and/or hyperchaotic systems under linear coupling. More generally, the conditional Lyapunov exponents are often calculated to confirm the stability of synchronization and reliability of linear controllers. In this paper, detailed proof and measurement of the reliability of linear controllers are given by constructing a Lyapunov function in the exponential form. It is confirmed that two hyperchaotic systems can reach complete synchronization when two linear controllers are imposed on the driven system unidirectionally and the unknown parameters in the driving systems are estimated completely. Finally, it gives the general guidance to reach complete synchronization under linear coupling for other chaotic and hyperchaotic systems with unknown parameters.

Keywords: parameter estimation exponential Lyapunov function parameter observer linear coupling

Received: 19 February 2013
Revised: 01 April 2013
Accepted manuscript online:

PACS:

05.45.-a

(Nonlinear dynamics and chaos)

Fund: Project supported partially by the National Natural Science Foundation of China (Grant No. 11265008).

Corresponding Authors: Ma Jun
E-mail: hyperchaos@163.com

Cite this article:

Li Fan (李凡), Wang Chun-Ni (王春妮), Ma Jun (马军) Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters 2013 Chin. Phys. B 22 100502

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Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

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