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

Tianwei Zhang; Lijun Xu

Kybernetika (2019)

  • Volume: 55, Issue: 4, page 690-713
  • ISSN: 0023-5954

Abstract

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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 2th 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.

How to cite

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Zhang, Tianwei, and Xu, Lijun. "Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays." Kybernetika 55.4 (2019): 690-713. <http://eudml.org/doc/295071>.

@article{Zhang2019,
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 2th 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.},
author = {Zhang, Tianwei, Xu, Lijun},
journal = {Kybernetika},
keywords = {semi-discrete method; stochastic; Krasnoselskii's fixed point theorem; almost periodicity; global exponential stability},
language = {eng},
number = {4},
pages = {690-713},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays},
url = {http://eudml.org/doc/295071},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Zhang, Tianwei
AU - Xu, Lijun
TI - Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 4
SP - 690
EP - 713
AB - 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 2th 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.
LA - eng
KW - semi-discrete method; stochastic; Krasnoselskii's fixed point theorem; almost periodicity; global exponential stability
UR - http://eudml.org/doc/295071
ER -

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