Qualitative analysis of artificial neural networks with multiple delays

It is well known that a class of artificial neural networks with symmetric interconnections and without transmission delays, known as Cohen-Grossberg neural networks, possesses global stability (i.e., all trajectories tend to some equilibrium). The authors demonstrate in the present paper that many of the qualitative properties of Cohen-Grossberg networks will not be affected by the introduction of sufficiently small delays. Specifically, the authors establish some bound conditions for the time delays under which a given Cohen-Grossberg network with multiple delays is globally stable and possesses the same asymptotically stable equilibria as the corresponding network without delays. An effective method of determining the asymptotic stability of an equilibrium of a Cohen-Grossberg network with multiple delays is also presented.

[1]  C. Goffman,et al.  Calculus of Several Variables , 1965 .

[2]  Shigeo Abe,et al.  Neural Networks and Fuzzy Systems , 1996, Springer US.

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

[4]  Wolfgang Porod,et al.  Qualitative analysis and synthesis of a class of neural networks , 1988 .

[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]  I. Guyon,et al.  Information storage and retrieval in spin-glass like neural networks , 1985 .

[7]  Wang,et al.  Global stability and local stability of Hopfield neural networks with delays. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

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

[10]  A. Michel,et al.  Stability of nonlinear time-delay systems with parameter uncertainties with an application to neural networks , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[11]  J. Farrell,et al.  Qualitative analysis of neural networks , 1989 .

[12]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[13]  L. Personnaz,et al.  Collective computational properties of neural networks: New learning mechanisms. , 1986, Physical review. A, General physics.

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

[16]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

[17]  U. Heiden.  Analysis Of Neural Networks , 1980 .

[18]  Theodore A. Burton,et al.  Averaged neural networks , 1993, Neural Networks.

[19]  J J Hopfield,et al.  Collective computation in neuronlike circuits. , 1987, Scientific American.

[20]  L. Pandolfi,et al.  On stability of cellular neural networks with delay , 1993 .

[21]  B. D. Coleman,et al.  Periodic Solutions of Certain Nonlinear Integral Equations with a Time Lag , 1976 .

[22]  G Palm,et al.  Computing with neural networks. , 1987, Science.