Global stability analysis of neural networks with multiple time varying delays

In this note, we study the equilibrium and stability properties of neural networks with time varying delays. Our main results give sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point. The proposed conditions establish the relationships between network parameters of the neural systems and the delay parameters. The obtained results are applicable to all continuous nonmonotonic neuron activation functions and do not require the interconnection matrices to be symmetric. Some examples are also presented to compare our results with the previous results derived in the literature.

[1]  Réjean Plamondon,et al.  On the stability analysis of delayed neural networks systems , 2001, Neural Networks.

[2]  Kwong-Sak Leung,et al.  Convergence analysis of cellular neural networks with unbounded delay , 2001 .

[3]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[4]  Tianping Chen,et al.  Global exponential stability of delayed Hopfield neural networks , 2001, Neural Networks.

[5]  Anke Meyer-Bäse,et al.  Global Asymptotic Stability of a Class of Dynamical Neural Networks , 2003, Int. J. Neural Syst..

[6]  Zhanshan Wang,et al.  Global Asymptotic Stability of Delayed Cellular Neural Networks , 2007, IEEE Transactions on Neural Networks.

[7]  S. Arik,et al.  On the global asymptotic stability of delayed cellular neural networks , 2000 .

[8]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[9]  Jun Wang,et al.  Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks , 2002, IEEE Trans. Autom. Control..

[10]  Korris Fu-Lai Chung,et al.  Some sufficient conditions for global exponential stability of delayed Hopfield neural networks , 2004, Neural Networks.

[11]  Tianping Chen,et al.  Global convergence of delayed dynamical systems , 2001, IEEE Trans. Neural Networks.

[12]  Jin Xu,et al.  On the global stability of delayed neural networks , 2003, IEEE Trans. Autom. Control..

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

[14]  S. Arik,et al.  Equilibrium analysis of delayed CNNs , 1998 .

[15]  Norikazu Takahashi,et al.  A new sufficient condition for complete stability of cellular neural networks with delay , 2000 .

[16]  Teh-Lu Liao,et al.  Global stability for cellular neural networks with time delay , 2000, IEEE Trans. Neural Networks Learn. Syst..

[17]  Jiye Zhang,et al.  Global stability analysis of bidirectional associative memory neural networks with time delay , 2001, Int. J. Circuit Theory Appl..

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