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Adaptive Q-S synchronization between coupled chaotic systems with stochastic perturbation and delay. (English) Zbl 1252.93072

Summary: We investigate the adaptive Q-S synchronization of coupled chaotic (or hyper-chaotic) systems with stochastic perturbation, delay and unknown parameters. The sufficient conditions for achieving Q-S synchronization of two stochastic chaotic systems are derived based on the invariance principle of stochastic differential equation. By the adaptive control technique, the control laws and the corresponding parameter update laws are proposed such that the stochastic Q-S synchronization of non-identical chaotic (or hyper-chaotic) systems is to be obtained. Finally, two illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

MSC:

93C40 Adaptive control/observation systems
34H10 Chaos control for problems involving ordinary differential equations
34K50 Stochastic functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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