title: Multistability of neural networks with Mexican-hat-type activation functions.
abstract: In this paper, we are concerned with a class of neural networks with Mexican-hat-type activation functions. Due to the different structure from neural networks with saturated activation functions, a set of new sufficient conditions are presented to study the multistability, including the total number of equilibrium points, their locations, and stability. Furthermore, the attraction basins of stable equilibrium points are investigated for two-neuron neural networks. The investigation shows that the stable manifolds of unstable equilibrium points constitute the boundaries of attraction basins of stable equilibrium points. Several illustrative examples are given to verify the effectiveness of our results.
authors.forename: Lili
authors.initials: L
authors.lastname: Wang
authors.forename: Tianping
authors.initials: T
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D006801:Humans; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D013997:Time Factors