Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks

被引：21
|
作者：
Rathinasamy, A. [1 ]
Narayanasamy, J. [2 ]
机构：
[1] Anna Univ, Dept Math, Chennai 025, India
[2] PSG Coll Technol, Dept Math, Coimbatore 641004, Tamil Nadu, India
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 348卷
关键词：
Stochastic delay differential equations; Hopfield neural networks; Two step Maruyama methods; Mean square stability; Almost sure exponential stability; SEMIIMPLICIT EULER METHOD; DIFFERENTIAL-EQUATIONS; NUMERICAL-METHODS; SYSTEMS; STABILIZATION;
D O I：
10.1016/j.amc.2018.11.063
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the two-step Maruyama methods of stochastic delay Hopfield neural networks are studied. We have found that under what choices of step-size, the two-step Maruyama methods of stochastic delay Hopfield networks, maintain the stability of exact solutions. The mean-square stability of two-step Maruyama methods of stochastic delay Hopfield neural networks is investigated under suitable conditions. Also, the almost sure exponential stability of two-step Maruyama methods of stochastic delay Hopfield networks is proved using the semi-martingale convergence theorem. Further, the comparisons of stability conditions to the previous results in Liu and Zhu (2015), Rathinasamy (2012) and Ronghua et al. (2010) are given. Numerical experiments are provided to illustrate our theoretical results. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：126 / 152
页数：27
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