时标上一类具有广义激活函数的高阶递归神经网络系统的指数收敛性（英文）
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摘要
考虑了时标上一类具有广义激活函数的高阶递归神经网络系统(RNNs).使用数学分析技巧,获得了该系统零点指数收敛的一些充分条件.
In this paper,we consider a class of higher- order recurrent neural networks( RNNs) with general activation functions on time scales. By using the mathematical analysis techniques,some sufficient conditions are established for the exponential convergence at zero- point.
In this paper,we consider a class of higher- order recurrent neural networks( RNNs) with general activation functions on time scales. By using the mathematical analysis techniques,some sufficient conditions are established for the exponential convergence at zero- point.
引文
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[15]Yia X J,Shao J Y,Yu Y H,et al.New convergence behavior of high-order hopfield neural networks with time-varying coefficients[J].J Comput Appl Math,2008,219:216-222.
[16]Cao J D,Wang J.Absolute exponential stability of recurrent neural networks with Lipschitz continuous activation functions and time delays[J].Neural Networks,2004,17:379-390.
[17]Liu B W.New convergence behavior of solutions to Cohen-Grossberg neural networks with delays and time-varying coefficients[J].Phys Lett A,2008,372:117-123.
[18]Hu S Q,Wang J.Absolute exponential stability of a class of continuous-time recurrent neural networks[J].IEEE Transactions on Neural Networks,2003,14:35-45.
[19]Zhang H,Wang W T,Xiao B.Exponential convergence for high-order recurrent neural networks with a class of general activation functions[J].Appl Math Modell,2011,35:123-129.
[20]Arik S.Global asymptotic stability of a class of dynamical neural networks[J].IEEE Transactions on Circuits and Systems I,Fundamental Theory and Applications,2000,47:568-571.
[21]Cao J D,Wang J.Global asymptotic and robust stability of recurrent neural networks with time delays[J].IEEE Transactions on Circuits and Systems I,Regular Papers,2005,52:417-426.
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[2]Chen A P,Chen F L.Periodic solution to BAM neural network with delays on time scales[J].Neurocom-puting,2009,73:274-282.
[3]Liu B W,Huang L H.Positive almost periodic solutions for recurrent neural networks[J].Nonlinear Anal:RWA,2008(9):830-841.
[4]Huang H,Cao J,Wang J.Global exponential stability and periodic solutions of recurrent cellular neural networks with delays[J].Phys Lett A,2002(5/6):393-404.
[5]Cao J,Wang J.Global exponential stability and periodicity of recurrent neural networks with time delays[J].IEEE Trans Circuits Syst-I,2005,52(5):920-931.
[6]Zheng F Y,Zhou Z,Ma C Q.Periodic solutions for a delayed neural network model on a special time scale[J].Appl Math Lett,2010,23:571-575.
[7]Liu Y,Wang Z,Liu X.Global exponential stability of generalized recurrent neural networks with discrete and distributed delays[J].Neural Network,2006,19:667-675.
[8]Liu B W,Gong S H,Yi X J,et al.Convergence for a class of delayed recurrent neural networks without M-matrix condition[J].J Comput Appl Math,2009,233:137-141.
[9]Li L Q,Huang L H.Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations[J].Appl Math Modell,2009,33:4326-4336.
[10]Peng G Q,Huang L H.Exponential stability of hybrid stochastic recurrent neural networks with time-varying delays[J].Nonlinear Anal:Hybrid Systems,2008(2):1198-1204.
[11]Yu J J,Zhang K J,Fei S M.Exponential stability criteria for discrete-time recurrent neural networks with time-varying delay[J].Nonlinear Anal:RWA,2010(11):207-216.
[12]Anke Meyer-Base,Sergei Pilyugin,Axel Wismüller,Simon Foo.Local exponential stability of competitive neural networks with different time scales[J].Engineering Applications of Artificial Intelligence,2004,17:227-232.
[13]Liu B W.Exponential convergence for a class of delayed cellular neural networks with time-varying coefficients[J].Phys Lett A,2008,372:424-428.
[14]Li Y Q,Huang L H.Exponential convergence behavior of solutions to shunting inhibitory cellular neural networks with delays and time-varying coefficients[J].Math Comput Modell,2008,48:499-504.
[15]Yia X J,Shao J Y,Yu Y H,et al.New convergence behavior of high-order hopfield neural networks with time-varying coefficients[J].J Comput Appl Math,2008,219:216-222.
[16]Cao J D,Wang J.Absolute exponential stability of recurrent neural networks with Lipschitz continuous activation functions and time delays[J].Neural Networks,2004,17:379-390.
[17]Liu B W.New convergence behavior of solutions to Cohen-Grossberg neural networks with delays and time-varying coefficients[J].Phys Lett A,2008,372:117-123.
[18]Hu S Q,Wang J.Absolute exponential stability of a class of continuous-time recurrent neural networks[J].IEEE Transactions on Neural Networks,2003,14:35-45.
[19]Zhang H,Wang W T,Xiao B.Exponential convergence for high-order recurrent neural networks with a class of general activation functions[J].Appl Math Modell,2011,35:123-129.
[20]Arik S.Global asymptotic stability of a class of dynamical neural networks[J].IEEE Transactions on Circuits and Systems I,Fundamental Theory and Applications,2000,47:568-571.
[21]Cao J D,Wang J.Global asymptotic and robust stability of recurrent neural networks with time delays[J].IEEE Transactions on Circuits and Systems I,Regular Papers,2005,52:417-426.
[22]Balasubramaniam P,Rakkiyappan R.Global asymptotic stability of stochastic recurrent neural networks with multiple discrete delays and unbounded distributed delays[J].Appl.Math.Comput.2008,204:680-686.
[23]Hilger S.Analysis on measure chains-a unified approach to continuous and discrete calculus[J].Results in Mathematics,1990,18:18-56.
[24]Hilger S.Differential and difference calculus-unified[J].Nonlinear Anal,1997,30:2683-2694.
[25]Agarwal R P,Bohner M,O’Regan D,Peterson A.Dynamic equations on time scales,a survey[J].J Comput Appl Math,2002,141:1-26.
[26]Bohner M,Peterson A.Dynamic Equations on Time Scales,An Introduction with Applications[M].Birkhuser,Boston,2001.
[27]Bohner M,Peterson A.Advances in Dynamic Equations on Time Scales[M].Birkhuser,Boston,2003.