Pseudo Almost Automorphic Solutions of Recurrent Neural Networks with Time-Varying Coefficients and Mixed Delays

In this paper, existence, uniqueness and global exponential stability of pseudo almost automorphic solutions for a class of recurrent neural networks with time-varying coefficients and mixed delays are established by employing the fixed point theorem and differential inequality. Numerical example with graphical illustration is given to illuminate our main results.

[1]  Yonghui Xia,et al.  Almost Automorphic Solutions of Impulsive Cellular Neural Networks with Piecewise Constant Argument , 2014, Neural Processing Letters.

[2]  Chuanzhi Bai,et al.  Global stability of almost periodic solutions of Hopfield neural networks with neutral time-varying delays , 2008, Appl. Math. Comput..

[3]  Jin Liang,et al.  Some properties of pseudo-almost automorphic functions and applications to abstract differential equations , 2009 .

[4]  Farouk Chérif,et al.  Sufficient Conditions for Global Stability and Existence of Almost Automorphic Solution of a Class of RNNs , 2014 .

[5]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Adel M. Alimi,et al.  Asymptotic almost automorphic solutions of impulsive neural network with almost automorphic coefficients , 2014, Neurocomputing.

[7]  Syed Abbas Pseudo almost automorphic solutions of some nonlinear integro-differential equations , 2011, Comput. Math. Appl..

[8]  Khalil Ezzinbi,et al.  Pseudo-almost-automorphic solutions to some neutral partial functional differential equations in Banach spaces , 2009 .

[9]  Gaston M. N'Guérékata,et al.  Topics in Almost Automorphy , 2004 .

[10]  Jinde Cao,et al.  Almost periodic solutions of recurrent neural networks with continuously distributed delays , 2009 .

[11]  Jin Liang,et al.  Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces , 2008 .

[12]  Jinde Cao,et al.  Exponential stability of high-order bidirectional associative memory neural networks with time delays , 2004 .

[13]  Adel M. Alimi,et al.  Existence and Uniqueness of Pseudo Almost-Periodic Solutions of Recurrent Neural Networks With Time-Varying Coefficients and Mixed Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Chuanyi Zhang,et al.  Integration of vector-valued pseudo-almost periodic functions , 1994 .

[15]  S Bochner,et al.  CONTINUOUS MAPPINGS OF ALMOST AUTOMORPHIC AND ALMOST PERIODIC FUNCTIONS. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Chuanzhi Bai,et al.  Existence and stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays , 2009 .

[17]  Khalil Ezzinbi,et al.  Exponential dichotomy and pseudo-almost automorphy for partial neutral functional differential equations , 2009 .

[18]  Jin Liang,et al.  Composition of pseudo almost automorphic and asymptotically almost automorphic functions , 2008 .

[19]  Yong Li,et al.  Alternative Theorems for Pseudo Almost Automorphic Problems , 2011 .

[20]  Chuanyi Zhang Pseudo Almost Periodic Solutions of Some Differential Equations, II , 1994 .