Stability of Recurrent Cellular Neural Networks with Variable Time Delays
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摘要: 利用M-矩阵理论和矢量Lyapunov函数方法,研究变时滞周期运动细胞神经网络的全局指数稳定性.在放松该类神经网络激活函数的有界性、单调递增性、可微性及Lipschitz连续等条件下,得到了该类神经网络周期解的存在性与全局指数稳定的代数判据.该判据基于神经网络激活函数满足的条件,利用连接权值矩阵及阻尼系数矩阵构造测试矩阵,根据测试矩阵是否为M-矩阵判定系统周期解的存在性与全局指数稳性.Abstract: The global exponential stability of a class of recurrent cellular neural networks with variable time delays was studied using M-matrix theory and vector Lyapunov methods.Without assuming the boundedness,monotonicity,differentiability and Lipschitz continuity of the active functions,an algebraic criterion to ensure existence and globally exponential stability of periodic solutions was obtained.From the weight matrix and damping coefficient matrix of the neural networks,a test matrix was constructed based on the conditions satisfied by the active functions.A recurrent cellular neural network has periodic and globally exponential stable solutions if the test matrix is an M-matrix.
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Key words:
- neural network /
- variable time delay /
- periodic solution /
- exponential stability /
- M-matrix
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CHUA L O,YANG L.Cellular neural networks:theory[J].IEEE Transactions on Circuits and Systems,1988,35(10):1 257-1 272.[2] FORTI M,TESI A.New conditions for global stability of neural networks with app] ication to linear and quadratic programming problems[J].IEEE Transactions on Cirenits and Systems -Ⅰ:Fundamental Theory and Applications,1995,42 (7):354-366.[3] ZHANG J,JIN X.Global stability analysis in delayed Hopfield neural networks models[J].Neural Networks,2000,13(7):745-753.[4] 谭晓惠,张继业,杨翊仁.Hopfield神经网络的全局指数稳定性[J].西南交通大学报,2005,40(3):338-342.TAN Xiaohui,ZHANG Jiye,YANG Yircn.Global exponential stability of hopfield neural networks[J].Journal of Southwest Jisotong University,2005,40 (3):338-342.[5] KOLMANOVSKII V B,MYSHIS A.Introduction to the theory and applications of funetiunal differential equations[M].Dordrecht:Kluwer Academic Publishers,1999:489-519.[6] BURTON T A.Stability and periodic solutions of ordinary and functional differential equations[M].Orlando:Academic Press,1985:197-324.[7] LI Yongkun,KUANG Yang.Periodic solutions of periodic delay on Lotka-Volterra equations and systems[J].Journal of Mathematical Analysis Applications,2001,255 (1):260-280.[8] CAO Jinde.New result concerning exponential stability and periodic solutions of delayed cellular neural networks[J].Physics Letters A,2003,307(2-3):136-147.[9] CAO Jinde.Periodic oscillation and exponential stability of delayed CNNs[J].Physics Letters A,2000,270(3-4):157-163.[10] LIU Zhigang,CHEN Anping,CAO Jinde,et al.Existance and global exponential stability of periodic solution for BAM neural networks with periodic eoefficients and time-varying delays[J].IEEE Transactions on Circuits and Systems-Ⅰ:Fundamental Theory and Applications,2003,50(9):1 162-1 172.[11] CHEN Anping,CAO Jinde.Existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients[J].Applied Mathematics and Computation,2003,134(1):125-140.[12] 舒仲周,张继业,曹登庆.运动稳定性[M].北京:中国铁道出版社,2001:79-126.[13] SILJAK D D.Large-scale dynamic systems:stability and structure[M].New York:Elsevier Noah-Holland,1978:100-120.
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