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

页码：126 / 152

页数：27

共 50 条

[41] Stability of Stochastic -Methods for Stochastic Delay Hopfield Neural Networks Under Regime Switching
Jiang, Feng
Shen, Yi
NEURAL PROCESSING LETTERS, 2013, 38 (03) : 433 - 444
[42] Generalized exponential stability of stochastic Hopfield neural networks with variable coefficients and infinite delay
Ruan, Dehao
Lu, Yao
AIMS MATHEMATICS, 2024, 9 (08): : 22910 - 22926
[43] Almost sure exponential stability and stochastic stabilization of impulsive stochastic differential delay equations
Liu, Xin
Cheng, Pei
Cui, Yao
SYSTEMS & CONTROL LETTERS, 2024, 187
[44] New mean square exponential stability condition of stochastic fuzzy neural networks
Xing, Xing
Pan, Yingnan
Lu, Qing
Cui, Hongxia
NEUROCOMPUTING, 2015, 156 : 129 - 133
[45] Mean square exponential stability of a class of neutral stochastic delayed neural networks
Qu Yi
Ma Qian
Zhang Yi-jun
2013 32ND CHINESE CONTROL CONFERENCE (CCC), 2013, : 3269 - 3274
[46] Mean square exponential stability of stochastic fuzzy Hopfield neural networks with discrete and distributed time-varying delays
Li, Hongyi
Chen, Bing
Lin, Chong
Zhou, Qi
NEUROCOMPUTING, 2009, 72 (7-9) : 2017 - 2023
[47] Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays
Ma, Li
Da, Feipeng
PHYSICS LETTERS A, 2009, 373 (25) : 2154 - 2161
[48] Mean square exponential stability of stochastic high-order Hopfield neural networks with time-varying delays
Shi, Xiangdong
SENSORS, MEASUREMENT AND INTELLIGENT MATERIALS, PTS 1-4, 2013, 303-306 : 1532 - 1535
[49] Almost sure exponential stability of stochastic fluid networks with nonlinear control
Zhu, Song
Chang, Wenting
Liu, Dan
INTERNATIONAL JOURNAL OF CONTROL, 2018, 91 (02) : 400 - 410
[50] Mean square exponential stability of stochastic nonlinear delay systems
Zhu, Quanxin
Song, Shiyun
Tang, Tianren
INTERNATIONAL JOURNAL OF CONTROL, 2017, 90 (11) : 2384 - 2393

← 1 2 3 4 5 →