Global exponential stability and existence of periodic solutions for delayed reaction-diffusion BAM neural networks with Dirichlet boundary conditions

被引：6
作者：
Zhang, Weiyuan [1 ]
Li, Junmin [2 ]
Chen, Minglai [2 ]
机构：
[1] Xianyang Normal Univ, Inst Math & Appl Math, Xianyang 712000, Peoples R China
[2] Xidian Univ, Sch Sci, Xian 710071, Shaanxi, Peoples R China
来源：
BOUNDARY VALUE PROBLEMS | 2013年
基金：
中国国家自然科学基金;
关键词：
neural networks; reaction-diffusion; mixed time delays; global exponential stability; Poincare mapping; Lyapunov functional; TIME-VARYING DELAYS; DISTRIBUTED DELAYS; ASYMPTOTIC STABILITY; OSCILLATORY SOLUTION; TERMS; CRITERION;
D O I：
10.1186/1687-2770-2013-105
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, both global exponential stability and periodic solutions are investigated for a class of delayed reaction-diffusion BAM neural networks with Dirichlet boundary conditions. By employing suitable Lyapunov functionals, sufficient conditions of the global exponential stability and the existence of periodic solutions are established for reaction-diffusion BAM neural networks with mixed time delays and Dirichlet boundary conditions. The derived criteria extend and improve previous results in the literature. A numerical example is given to show the effectiveness of the obtained results.
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页数：23
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共 34 条
[21]   Global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms [J].
Song, QK ;
Zhao, ZJ ;
Li, YM .
PHYSICS LETTERS A, 2005, 335 (2-3) :213-225
[22]   Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms [J].
Song, QK ;
Cao, JD .
CHAOS SOLITONS & FRACTALS, 2005, 23 (02) :421-430
[23]   Global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms [J].
Wang, Jian ;
Lu, Jun Guo .
CHAOS SOLITONS & FRACTALS, 2008, 38 (03) :878-885
[24]   Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays [J].
Wang, Linshan ;
Zhang, Ruojun ;
Wang, Yangfan .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (02) :1101-1113
[25]   An LMI Approach to Stability Analysis of Reaction-Diffusion Cohen-Grossberg Neural Networks Concerning Dirichlet Boundary Conditions and Distributed Delays [J].
Wang, Zhanshan ;
Zhang, Huaguang ;
Li, Ping .
IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS, 2010, 40 (06) :1596-1606
[26]   Global Asymptotic Stability of Reaction-Diffusion Cohen-Grossberg Neural Networks With Continuously Distributed Delays [J].
Wang, Zhanshan ;
Zhang, Huaguang .
IEEE TRANSACTIONS ON NEURAL NETWORKS, 2010, 21 (01) :39-49
[27]   Exponential convergence of BAM neural networks with time-varying coefficients and distributed delays [J].
Wu, Ranchao .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (01) :562-573
[28]   Global exponential stability of reaction-diffusion neural networks with discrete and distributed time-varying delays [J].
Zhang Wei-Yuan ;
Li Jun-Min .
CHINESE PHYSICS B, 2011, 20 (03)
[29]   Dynamical Behaviors of Impulsive Stochastic Reaction-Diffusion Neural Networks with Mixed Time Delays [J].
Zhang, Weiyuan ;
Li, Junmin ;
Chen, Minglai .
ABSTRACT AND APPLIED ANALYSIS, 2012,
[30]   Stability Analysis for Stochastic Markovian Jump Reaction-Diffusion Neural Networks with Partially Known Transition Probabilities and Mixed Time Delays [J].
Zhang, Weiyuan ;
Li, Junmin ;
Shi, Naizheng .
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2012, 2012
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