A note on stability of analog neural networks with time delays

This note presents a generalized sufficient condition which guarantees stability of analog neural networks with time delays. The condition is derived using a Lyapunov functional and the stability criterion is stated as: the equilibrium of analog neural networks with delays is globally asymptotically stable if the product of the norm of connection matrix and the maximum neuronal gain is less than one.

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

[2]  Jack K. Hale,et al.  Nonlinear Oscillations in Equations with Delays. , 1978 .

[3]  Bor-Sen Chen,et al.  Robust stability of uncertain time-delay systems , 1987 .

[4]  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.

[5]  Charles M. Marcus,et al.  Nonlinear dynamics and stability of analog neural networks , 1991 .

[6]  John S. Denker Neural networks for computing : Snowbird, UT 1986 , 1986 .

[7]  L. Wang,et al.  Oscillations and chaos in neural networks: an exactly solvable model. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Schuster,et al.  Collective frequencies and metastability in networks of limit-cycle oscillators with time delay. , 1991, Physical review letters.

[9]  J. Hale Retarded equations with infinite delays , 1979 .

[10]  Amir F. Atiya,et al.  How delays affect neural dynamics and learning , 1994, IEEE Trans. Neural Networks.

[11]  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.