Kybernetika 55 no. 4, 690-713, 2019

Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays

Tianwei Zhang and Lijun XuDOI: 10.14736/kyb-2019-4-0690

Abstract:

By using the semi-discrete method of differential equations, a new version of discrete analogue of stochastic shunting inhibitory cellular neural networks (SICNNs) is formulated, which gives a more accurate characterization for continuous-time stochastic SICNNs than that by Euler scheme. Firstly, the existence of the $2p$th mean almost periodic sequence solution of the discrete-time stochastic SICNNs is investigated with the help of Minkowski inequality, Hölder inequality and Krasnoselskii's fixed point theorem. Secondly, the moment global exponential stability of the discrete-time stochastic SICNNs is also studied by using some analytical skills and the proof of contradiction. Finally, two examples are given to demonstrate that our results are feasible. By numerical simulations, we discuss the effect of stochastic perturbation on the almost periodicity and global exponential stability of the discrete-time stochastic SICNNs.

Keywords:

semi-discrete method, stochastic, Krasnoselskii's fixed point theorem, almost periodicity, global exponential stability

Classification:

39A50, 39A24, 39A30, 92B20

paper.pdf

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