Abstract
Since noise is ubiquitous in both nature and artificial systems, the stochastic perturbation influence on the dynamics of the unidirectionally coupled Ikeda models is investigated in this paper. On the one hand, sufficient conditions on the complete synchronization between these noise-perturbed and chaotic models are mathematically established, and an estimation of the sample transverse Lyapunov exponent is rigorously derived. On the other hand, specific examples and their numerical simulations are provided to illustrate the feasibility of our theoretical results. Moreover, the results on the Ikeda models are further generalized to a wide class of coupled nonlinear systems with multiple time delays and a common additive noise. It is believed that the idea and approach developed in this paper could be further generalized to investigate some other problems on chaos synchronization and chaos control with stochastic perturbation.
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