Abstract
In this paper, we deal with the adaptive stochastic synchronization for a class of delayed reaction–diffusion neural networks. By combing Lyapunov–Krasovskii functional, drive-response concept, the adaptive feedback control scheme, and linear matrix inequality method, we derive some sufficient conditions in terms of linear matrix inequalities ensuring the stochastic synchronization of the addressed neural networks. The output coupling with delay feedback and the update laws of parameters for adaptive feedback control are proposed, which will be of significance in the real application. The novel Lyapunov–Krasovskii functional to be constructed is more general. The derived results depend on the measure of the space, diffusion effects, and the upper bound of derivative of time-delay. Finally, an illustrated example is presented to show the effectiveness and feasibility of the proposed scheme.
Highlights
During the past two decades, chaos synchronization has been widely studied since it was introduced by Pecora and Carroll1 in 1990
Motivated by the above works, we develop the idea to a class of coupled delayed stochastic reaction–diffusion neural networks (RDNNs)
In Theorem 1, we propose the adaptive synchronization for a class of stochastic RDNNs with time-varying delays and unbounded distributed delays
Summary
During the past two decades, chaos synchronization has been widely studied since it was introduced by Pecora and Carroll in 1990. It is important to consider stochastic effects to the chaos synchronization control of NNs with delays. We will investigate the adaptive stochastic synchronization of RDNNs with mixed time delays. D(t) denotes the time-varying delay, and d(t) is assumed to satisfy 04d(t)4d and 04d0(t)4m \ 1, where d and m are constants; K(t À s) = diag 1⁄2k1(t À s), . Li et al. investigated the synchronization analysis of a class of delayed chaotic ordinary differential NNs with stochastic perturbations and designed the control input uÃ(t) = K1f(e(t)) + K2f(e(t À d(t))), where K1 and K2 are the gain matrices to be scheduled. Activation functions fj(Á) are bounded and fj(0) = 0; there exists a positive diagonal matrix L = diag(L1, . The terms V2(t) and V3(t) extend the constructions of the literature. The term V5(t) is added to V(t) to treat the distributed delay
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