Dynamic behavior of nonautonomous cellular neural networks with time-varying delays

In this paper, we investigate the dynamic behavior of nonautonomous cellular neural networks with time-varying delays. We firstly develop a differential inequality which plays an important role in study of boundedness, attracting set and stability of differential systems and improves some early Halanay-type inequalities. Based on the new inequality, the boundedness, attracting set, exponential stability and existence of periodic solution of the considered neural networks are obtained. Our results improve the early results in the literature. One example is given to illustrate the correctness and superiority of our conclusion.

[1]  Weigao Ge,et al.  Existence and uniqueness of periodic solutions of nonautonomous cellular neural networks with impulses , 2006 .

[2]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[3]  Minghui Jiang,et al.  Stability analysis in Lagrange sense for a non-autonomous Cohen-Grossberg neural network with mixed delays , 2009 .

[4]  Zhiqiang Zuo,et al.  On exponential stability analysis for neural networks with time-varying delays and general activation functions , 2012 .

[5]  Daoyi Xu,et al.  Attracting and quasi-invariant sets of non-autonomous neural networks with delays , 2012, Neurocomputing.

[6]  Daoyi Xu,et al.  Global exponential stability of non-autonomous cellular neural networks with impulses and time-varying delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[7]  Liping Wen,et al.  Generalized Halanay inequalities for dissipativity of Volterra functional differential equations , 2008 .

[8]  Yi Shen,et al.  Stability of non-autonomous bidirectional associative memory neural networks with delay , 2008, Neurocomputing.

[9]  Daoyi Xu,et al.  Delay-dependent stability analysis for impulsive neural networks with time varying delays , 2008, Neurocomputing.

[10]  Jinde Cao.  Global stability conditions for delayed CNNs , 2001 .

[11]  Weigao Ge,et al.  Periodic solutions of nonautonomous cellular neural networks with impulses , 2007 .

[12]  Xiaohu Wang,et al.  Attracting and invariant sets of non-autonomous reaction-diffusion neural networks with time-varying delays , 2012, Math. Comput. Simul..

[13]  Zhanji Gui,et al.  Periodic solutions of nonautonomous cellular neural networks with impulses and delays , 2009 .

[14]  Xuyang Lou,et al.  Boundedness and exponential stability for nonautonomous RCNNs with distributed delays , 2007, Comput. Math. Appl..

[15]  Jinde Cao,et al.  Global exponential stability of delayed cellular neural networks with impulses , 2007, Neurocomputing.

[16]  Sabri Arik,et al.  An analysis of global asymptotic stability of delayed cellular neural networks , 2002, IEEE Trans. Neural Networks.

[17]  Zhidong Teng,et al.  Boundedness and global stability for nonautonomous recurrent neural networks with distributed delays , 2006 .

[18]  Hongyong Zhao,et al.  Boundedness and stability of nonautonomous cellular neural networks with reaction-diffusion terms , 2009, Math. Comput. Simul..

[19]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[20]  Zhidong Teng,et al.  Boundedness and stability for nonautonomous cellular neural networks with delay , 2003, Neural Networks.

[21]  Qinghua Zhou,et al.  Asymptotic behaviors of stochastic Cohen-Grossberg neural networks with mixed time-delays , 2013, Appl. Math. Comput..

[22]  Daoyi Xu,et al.  Global exponential p-stability of stochastic non-autonomous Takagi-Sugeno fuzzy cellular neural networks with time-varying delays and impulses , 2014, Fuzzy Sets Syst..

[23]  Hong Zhang,et al.  Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms , 2013, Appl. Math. Comput..

[24]  Daoyi Xu,et al.  Global dynamics for non-autonomous reaction-diffusion neural networks with time-varying delays , 2008, Theor. Comput. Sci..

[25]  Qiang Zhang,et al.  Global exponential stability for nonautonomous cellular neural networks with delays , 2006 .

[26]  Xuyang Lou,et al.  Boundedness and exponential stability for nonautonomous cellular neural networks with reaction–diffusion terms , 2007 .

[27]  Zhidong Teng,et al.  Boundedness and exponential stability for nonautonomous FCNNs with distributed delays and reaction-diffusion terms , 2010, Neurocomputing.

[28]  L.O. Chua,et al.  Cellular neural networks , 1993, 1988., IEEE International Symposium on Circuits and Systems.

[29]  Pin-Lin Liu,et al.  Delay-dependent global exponential robust stability for delayed cellular neural networks with time-varying delay. , 2013, ISA transactions.

[30]  Jinde Cao,et al.  Boundedness and stability for recurrent neural networks with variable coefficients and time-varying delays , 2003 .

[31]  Hongjiong Tian.  The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag , 2002 .

[32]  J. Hale.  Functional Differential Equations , 1971 .

[33]  Yinping Zhang,et al.  Stationary oscillation for nonautonomous bidirectional associative memory neural networks with impulse , 2009 .