Title :
Multistability of Neural Networks With Mexican-Hat-Type Activation Functions
Author :
Lili Wang ; Tianping Chen
Author_Institution :
Dept. of Appl. Math., Shanghai Univ. of Finance & Econ., Shanghai, China
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.
Keywords :
neural nets; transfer functions; Mexican-hat-type activation functions; equilibrium point stable manifolds; neural network multistability; stable equilibrium point attraction basins; two-neuron neural networks; Biological neural networks; Indexes; Learning systems; Stability criteria; Trajectory; Attraction basin; Mexican-hat activation; multistability; neural networks; stability analysis;
Journal_Title :
Neural Networks and Learning Systems, IEEE Transactions on
DOI :
10.1109/TNNLS.2012.2210732