Abstract
Stochastic effects on convergence dynamics of reaction-diffusion Cohen-Grossberg neural networks (CGNNs) with delays are studied. By utilizing Poincare inequality, constructing suitable Lyapunov functionals, and employing the method of stochastic analysis and nonnegative semimartingale convergence theorem, some sufficient conditions ensuring almost sure exponential stability and mean square exponential stability are derived. Diffusion term has played an important role in the sufficient conditions, which is a preeminent feature that distinguishes the present research from the previous. Two numerical examples and comparison are given to illustrate our results.
Highlights
In the recent years, the problems of stability of delayed neural networks have received much attention due to its potential application in associative memories, pattern recognition and optimization
The results show that diffusion terms have contributed to the almost surely and mean square exponential stability criteria
In 35, Wan and Zhou have studied the problem of convergence dynamics of model 2.1 with the Neumann boundary condition and obtained the following result see 35, Theorem 3.1
Summary
The problems of stability of delayed neural networks have received much attention due to its potential application in associative memories, pattern recognition and optimization. Many interesting results on stochastic effects to the stability of delayed neural networks have been reported see 16–23. Based on the above discussion, it is significant and of prime importance to consider the stochastic effects on the stability property of the delayed reaction-diffusion networks. Sun et al 32, 33 have studied the problem of the almost sure exponential stability and the moment exponential stability of an equilibrium solution for stochastic reaction-diffusion recurrent neural networks with continuously distributed delays and constant delays, respectively. In 36 , the problem of stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters have been investigated.
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