Stability of non-autonomous bidirectional associative memory neural networks with delay

The paper discusses the stability of non-autonomous bidirectional associative memory neural networks. The existence and uniqueness of periodic solutions of the neural networks are investigated by using Gaines and Mawhin's continuation theorem of coincidence degree theory in the paper. Moreover, criterions on asymptotic stability and exponential stability of periodic solutions of the neural networks are obtained by using matrix function inequality, and algorithms for the criterions on the neural networks are provided. Some of the results in the paper generalize and improve the results in the existing references. In the end, an illustrate example is given to verify our results.

[1]  Sabri Arik,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays , 2005, IEEE Transactions on Neural Networks.

[2]  Xiaofeng Liao,et al.  Novel stability criteria for bidirectional associative memory neural networks with time delays , 2002, Int. J. Circuit Theory Appl..

[3]  Hongyong Zhao.  Global stability of bidirectional associative memory neural networks with distributed delays , 2002 .

[4]  Ju H. Park.  A novel criterion for global asymptotic stability of BAM neural networks with time delays , 2006 .

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

[6]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[7]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[8]  Jinde Cao,et al.  Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays , 2006 .

[9]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[10]  Juebang Yu,et al.  Qualitative analysis of Bi‐directional Associative Memory with time delay , 1998 .

[11]  Jinde Cao,et al.  Boundedness and stability for Cohen–Grossberg neural network with time-varying delays☆ , 2004 .

[12]  Jinde Cao,et al.  Exponential stability of periodic solution to Cohen-Grossberg-type BAM networks with time-varying delays , 2009, Neurocomputing.

[13]  N. Rouche,et al.  Ordinary differential equations : stability and periodic solutions , 1980 .

[14]  Libin Rong,et al.  LMI approach for global periodicity of neural networks with time-varying delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[15]  Réjean Plamondon,et al.  Stability analysis of bidirectional associative memory networks with time delays , 2003, IEEE Trans. Neural Networks.

[16]  Vedat Tavsanoglu,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays , 2005, Neurocomputing.

[17]  Kwok-Wo Wong,et al.  Robust stability of interval bidirectional associative memory neural network with time delays , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Zhidong Teng,et al.  Boundedness and stability for nonautonomous bidirectional associative neural networks with delay , 2004, IEEE Trans. Circuits Syst. II Express Briefs.

[19]  Yi Shen,et al.  Global stability of periodic solution for bidirectional associative memory neural networks with varying-time delay , 2006, Appl. Math. Comput..

[20]  Zhang Yi,et al.  Convergence Analysis of Recurrent Neural Networks , 2003, Network Theory and Applications.

[21]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.

[22]  Jinde Cao,et al.  LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay , 2007 .

[23]  E. I. El-Masry,et al.  A switched capacitor bidirectional associative memory , 1990 .

[24]  S. Mohamad.  Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks , 2001 .

[25]  Vimal Singh,et al.  A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks , 2004, IEEE Transactions on Neural Networks.