On the stability analysis of delayed neural networks systems

In this paper, the problems of stability of delayed neural networks are investigated, including the stability of discrete and distributed delayed neural networks. Under the generalization of dropping the Lipschitzian hypotheses for output functions, some stability criteria are obtained by using the Liapunov functional method. We do not assume the symmetry of the connection matrix and we establish that the system admits a unique equilibrium point in which the output functions do not satisfy the Lipschitz conditions and do not require them to be differential or strictly monotonously increasing. These criteria can be used to analyze the dynamics of biological neural systems or to design globally stable artificial neural networks.

[1]  Morris W. Hirsch,et al.  Convergent activation dynamics in continuous time networks , 1989, Neural Networks.

[2]  Tomoki Fukai,et al.  A subthreshold MOS circuit for the Lotka-Volterra neural network producing the winners-share-all solution , 1999, Neural Networks.

[3]  Christopher J. Bishop,et al.  Pulsed Neural Networks , 1998 .

[4]  V. Sree Hari Rao,et al.  Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones , 1999, Neural Networks.

[5]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[6]  Xuesong Jin,et al.  Global stability analysis in delayed Hopfield neural network models , 2000, Neural Networks.

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

[8]  Bart Kosko,et al.  Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence , 1991 .

[9]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[10]  R. D. Driver,et al.  A Uniqueness Theorem for Ordinary Differential Equations , 1981 .

[11]  N. K. Bose,et al.  Neural Network Fundamentals with Graphs, Algorithms and Applications , 1995 .

[12]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[13]  Jinde Cao,et al.  Stability analysis of delayed cellular neural networks , 1998, Neural Networks.

[14]  K. Gopalsamy,et al.  Stability in asymmetric Hopfield nets with transmission delays , 1994 .

[15]  Liang Jin,et al.  Globally asymptotical stability of discrete-time analog neural networks , 1996, IEEE Trans. Neural Networks.

[16]  Guanrong Chen,et al.  On delayed impulsive Hopfield neural networks , 1999, Neural Networks.

[17]  Yuguang Fang,et al.  Stability analysis of dynamical neural networks , 1996, IEEE Trans. Neural Networks.