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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 satur...Show More

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.
Published in: IEEE Transactions on Neural Networks and Learning Systems ( Volume: 23, Issue: 11, November 2012)
Page(s): 1816 - 1826
Date of Publication: 03 October 2012

ISSN Information:

PubMed ID: 24808075

References

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