A new result on the global convergence of Hopfield neural networks

In this work, we discuss Hopfield neural networks, investigating their global stability. Some sufficient conditions for a class of Hopfield neural networks to be globally stable and globally exponentially stable are given.

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

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

[3]  Shun-ichi Amari,et al.  Characteristics of randomly connected threshold-element networks and network systems , 1971 .

[4]  S. Amari,et al.  Characteristics of Random Nets of Analog Neuron-Like Elements , 1972, IEEE Trans. Syst. Man Cybern..

[5]  D. Kelly,et al.  Stability in contractive nonlinear neural networks , 1990, IEEE Transactions on Biomedical Engineering.

[6]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[7]  Zhang Yi,et al.  Estimate of exponential convergence rate and exponential stability for neural networks , 1999, IEEE Trans. Neural Networks.

[8]  E. Kaszkurewicz,et al.  On a class of globally stable neural circuits , 1994 .

[9]  M. Forti,et al.  Necessary and sufficient condition for absolute stability of neural networks , 1994 .

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

[11]  Kiyotoshi Matsuoka,et al.  Stability conditions for nonlinear continuous neural networks with asymmetric connection weights , 1992, Neural Networks.

[12]  Sommers,et al.  Chaos in random neural networks. , 1988, Physical review letters.

[13]  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.

[14]  Xue-Bin Liang,et al.  Global exponential stability of a class of neural circuits , 1999 .

[15]  Shun-ichi Amari,et al.  Stability of asymmetric Hopfield networks , 2001, IEEE Trans. Neural Networks.

[16]  Tharam S. Dillon,et al.  Exponential stability and oscillation of Hopfield graded response neural network , 1994, IEEE Trans. Neural Networks.

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

[19]  Shun-ichi Amari,et al.  New theorems on global convergence of some dynamical systems , 2001, Neural Networks.