Title :
Uniqueness and stability of equilibria of a class of neural networks with applications to the Hopfield model
Author :
Feng, Zhaoshu ; Michel, Anthony N.
Author_Institution :
Dept. of Electr. Eng., Notre Dame Univ., IN, USA
Abstract :
In this paper, new conditions for the existence and uniqueness of equilibria of a class of continuous-time recurrent neural networks are established by utilizing the Brouwer fixed point theorem and results from homotopy theory. Also, new criteria are established for the local and global asymptotic stability of the equilibrium of neural networks with non-symmetric and symmetric interconnecting matrices, respectively. The present results are applied to the Hopfield continuous-time neural networks
Keywords :
Hopfield neural nets; asymptotic stability; circuit stability; differential equations; matrix algebra; Brouwer fixed point theorem; Hopfield neural networks; asymptotic stability; continuous-time neural networks; differential equations; homotopy theory; matrix algebra; recurrent neural networks; uniqueness; Asymptotic stability; Differential equations; Hopfield neural networks; Intelligent networks; Jacobian matrices; Neural networks; Recurrent neural networks; Symmetric matrices;
Conference_Titel :
Decision and Control, 1997., Proceedings of the 36th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
0-7803-4187-2
DOI :
10.1109/CDC.1997.652470
