期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
S-分布时滞随机高阶Hopfield神经网络的均方指数稳定性
- 中国海洋大学 数学科学学院, 山东 青岛 266100
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DOI：10.13763/j.cnki.jhebnu.nse.2015.04.003
The Mean Square Exponential Stability of Stochastic High Order Hopfield Neural Networks with S-type Distributed Time Delays
摘要/Abstract
摘要：
考虑了一类具有S-分布时滞随机高阶Hopfield神经网络模型的动力行为.利用Lyapunov泛函方法、随机分析理论和不等式技巧,研究了网络的均方指数稳定性,给出了均方稳定性判据,并以实例证明了结论的正确性.
Abstract：
The dynamical behavior of the stochastic higher-order Hopfield-type neural networks with S-type distributed time delays is investigated in this paper.A criterion of exponential stability in the mean square is established with the Lyapunov functional method and stochastic analysis techniques. An example is given illustrate the validity of our results.
关键词
参考文献 20
- [1] HOPFIELD J J.Neural Networks and Physical System with Emergent Collective Computational Abilities[J].NationalAcademy of Sciences,1982,79(8):2554-2558.
- [2] HOPFIELD J J.Neurons with Graded Response Have Collective Computational Like Those of Two-state Neurons[J].Proceedings of the National Academy of Sciences,1984,81(10):3088-3092.
- [3] XU D Y,YANG X H.Further Results on Existence-uniqueness for Stochastic Functional Differential Equation[J].Science China Mathematics,2013,56:1169-1180.
- [4] LIAO X X,LIAO Y.Stability of Hopfield-type Neural Networks[J].Science in China Series A:Mathematics,1997,40(8):813-816.
- [5] WALLIS G.Stability Criteria for Unsupervised Temporal Association Networks[J].IEEE Transactions on Neural Networks,2005,16(2):301-311.
- [6] WANG C,HILL D J.Deterministic Learning and Rapid Dynamical Pattern Recognition[J].IEEE Transactions on Neural Networks,2007,18(3):617-630.
- [7] ZHOU J,LI S Y,YANG Z G.Global Exponential Stability of Hopfield Neural Networks with Distributed Delays[J].Applied Mathematical Modelling,2009,33(3):1513-1520.
- [8] GAN Q T,XU R.Global Robust Exponential Stability of Uncertain Neutral High-order Stochastic Hopfield Neural Networks with Time-varying Delays[J].Neural Processing Letters,2010,32:83-96.
- [9] LIU W,FU C,HU H.Global Exponential Stability of a Class of Hopfield Neural Networks with Delays[J].Neural Computing & Applications,2011,20(8):1205-1209.
- [10] WEI Y.Application of Competitive Hopfield Neural Network to Brain-computer Interface Systems[J].International Journal of Neural Systems,2012,22(1):51-62.
- [11] XU H L,CHEN Y Q,KOK L T.Global Exponential Stability of Impulsive Discrete-time Neural Networks with Time-varying Delays[J].Applied Mathematics and Computation,2010,217(2):537-544.
- [12] WANG Y F,LU C G,JI G R,et al.Global Exponential Stability of High-order Hopfield-type Neural Networks with S-type Distributed Time Delays[J].Communications in Nonlinear Science and Numerical Simulation,2011,16(8):3319-3325.
- [13] XU B J,LIU X Z,LIAO X X.Global Aysmptotic Stability of High-order Hopfield Type Neural Networks with Time Delays[J].Computers & Mathematics with Applications,2003,45(10):1729-1737.
- [14] WANG Z,FANG J,LIU X.Global Stability of Stochastic High-order Neural Networks with Discrete and Distributed Delays[J].Chaos,Solitons & Fractals,2008,36(2):388-396.
- [15] XIAO B,MENG H.Existence and Exponential Stability of Positive Almost Periodic Solutions for High-order Hopfield Neural Networks[J].Applied Mathematical Modelling,2009,33(1):532-542.
- [16] QIU J.Dynamics of High-order Hopfield Neural Networks with Time Delays[J].Neurocomputing,2010,73:820-826.
- [17] XU B J,XU Y,HE Linman.LMI-based Stability Analysis of Impulsive High-order Hopfield-type Neural Networks[J].Mathematics and Computers in Simulation,2012,86:67-77.
- [18] ZHANF B Y,XU S Y,LI Y M.On Global Exponential Stability of High-order Neural Networks with Time-varying Delays[J].Physics Letters A,2007,366:69-78.
- [19] 王林山.时滞递归神经网络[M].北京:科学出版社,2008.
- [20] MAO X R.Stochastic Differential Equation and Application[M].Chichester:Horwood Publishing Limited,1997.