蒋海军

• 1:新疆大学数学与系统科学学院

摘要(Abstract)：

研究了具有变系数和无穷时滞的双向联想记忆神经网络,通过引入相空间Cg(R_)×Cg(R_)和Lyapunov泛函方法,建立了一系列关于解的有界性和全局渐近稳定性的判别准则.对于具有变系数和无穷时滞周期的双向联想记忆神经网络,通过应用周期解存在定理,建立了该系统周期解存在和全局稳定的充分条件.将上述结果应用于自治双向联想记忆神经网络,得到了平衡点的存在性、唯一性和全局渐近稳定性.

关键词(KeyWords)： 双向联想记忆神经网络;无穷时滞;变系数;有界性;全局渐近稳定性;周期解;平衡点;Lyapunov泛函;Banach空间

Abstract:

Keywords:

基金项目(Foundation): supported by the National Natural Science Foundation of P.R.China(60764003);; the Major Project of The Ministry of Education of P.R.China and the Funded by Scientific Research Program of the HigherEducation Institution of Xinjiang(XJEDU2004I12 and XJEDU2006I05)

作者(Author): 蒋海军

参考文献(References)：

• [1]Arik S.An analysis of exponential stability of delayed neural networks with time varying delays[J].Neural networks,2004,17:1027-1031.
• [2]Burton T A.Stability and Periodic Solutions of Ordinary and Functional Differential Equations[M].New York:Academic Press INC,1985.
• [3]Burton T A,Grimmer R C.Oscillation,continuation and uniqueness of solutions of retarted differential equations[J]. Transactions American Mathematical Society,1973,179:193-209.
• [4]Burton T A,Zhang S.Unified bounded,periodicity,and stability in ordinary and functional differential equations[J]. Annali Mathematica Pure de Applicata,1986,145:129-158.
• [5]Cao J.New results concerning exponential stability and periodic solutions of delayed cellular neural networks[J].Physics Letters A,2003,307:136-147.
• [6]Cao J,Wang J.Global asymptotic stability of a general class of recurrent neural networks with time-varying delays[J]. IEEE Transactions on Circuits and Systems I,2003,50:34-44.
• [7]Cao J,Wang J.Global asymptotic and robust stability of recurrent neural networks with time delays[J].IEEE Trans Circuits Syst I,2005,52:417-426.
• [8]Cao J,Wang J.Exponential stability and periodic oscillatory solution in BAM networks with delays[J].IEEE Transactions on Neural Networks,2002,13:457-463.
• [9]Chen A,Cao J,Huang L.Exponential stability of BAM neural networks with transmission delays[J].Neurocomputing, 2004,57:435-454.
• [10]Chen Y.Global stability of neural networks with distributed delays[J].Neural Networks,2002,15:867-871.
• [11]Cheng Q,Zhang D,Yan G,Qian Z.Elements of the Real Valued Function and Functional Analysis[M].Higher Education Press,1983.
• [12]Dong M.Global exponential stability and existence of periodic solutions of CNNs with delays[J].Physics Letters A,2002, 300:49-57.
• [13]Dong Q,Matsui K,Huang X.Existence and stability of periodic solutions for Hopfield neural network equations with periodic input[J].Nonlinear Analysis,2002,49:471-479.
• [14]Guo S,Huang L,Dai B,Zhang Z.Global existence of periodic solutions of BAM neural networks with variable coeffcients[J]. Physics Letters A,2003,317:97-106.
• [15]Huang H,Cao J,Wang J.Global exponential stability and periodic solutions of recurrent neural networks with delays[J]. Physics Letters A,2002,298:393-404.
• [16]Hering R H.Boundedness and periodic solutions in infinite delay system[J].Journal Mathematics Analysis and Applica- tions,1992,163:521-537.
• [17]Jiang H,Li Z,Teng Z.Boundedness and stability for nonautonomous cellular neural networks with delay[J].Physics Letters A,2003,306:313-325.
• [18]Jiang H,Teng Z.Boundedness and stability for nonautonomous bidirectional associative neural networks with delay[J]. IEEE Trans Circuits and Sys II,2004,51:174-180.
• [19]Makay G.Periodic solutions of dissipative functional differential equations with infinite delay[J].Tohoku Mathematical Journal,1996,48:355-362.
• [20]Makay G.Periodic solutions of linear differential and integral equations[J].Differential and Integral Equations,1995,8: 2177-2187.
• [21]Peng J,Qiao H,Xu Z.A new approach to stability of neural networks with time-varying delays[J].Neural Networks,2002,15:95-103.
• [22]Xu S,Lam J,Ho D W C,Zou Y.Novel Global asymptotic stability criteria for delayed cellular neural networks[J].IEEE Trans Circuits Syst II,2005,52:349-353.
• [23]Zhang Bo.Boundedness in functional differential equations[J].Nonlinear Analysis,1994,22:1511-1527.
• [24]Zhou J,Liu Z,Chen G.Dynamics of periodic delayed neural networks[J].Neural Networks.2004,17:87-101.
• [25]Zhang Q,Wei X,Xu J.Global exponential stability of Hopfield neural networks with continuously distributed delays[J]. Physics Letters A,2003,315:431-436.
• [26]Zhang Y,Pheng H A,Leung K S.Convergence Analysis of Cellular Neural Networks with Unbounded Delay[J].IEEE Transactions on Circuits and Systems I,2001,48:680-687.