ANALYSIS OF A CLASS OF RECURRENT NEURAL NETWORKS WITH ARBITRARY EXPONENTS.

This paper deals with problems of stability and travelling waves for a class of recurrent neural networks with arbitrary exponents k and m. A novel model which is not only nonlinear but also coupled is proposed. This paper makes the following contributions: (1) Conditions for local stablility of 1-D networks and 2-D networks are established with a series of mathematical arguments. (2) Completely convergence of 1-D neural networks is proved by constructing a suitable energy function. (3) The nonuniform solution of the networks is obtained when the connectivity is Gaussian profile. (4) Travelling waves of the networks are analyzed with the connectivity profile. Finally, simulation examples are employed to illustrate the obtained results. [ABSTRACT FROM AUTHOR]