Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions
We investigate the existence and dynamical behaviors of multiple equilibria for competitive neural networks with a class of general Mexican-hat-type activation functions. The Mexican-hat-type activation functions are not monotonously increasing, and the structure of neural networks with Mexican-hat-...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/901519 |
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| Summary: | We investigate the existence and dynamical behaviors of multiple equilibria
for competitive neural networks with a class of general Mexican-hat-type activation
functions. The Mexican-hat-type activation functions are not monotonously increasing, and the
structure of neural networks with Mexican-hat-type activation functions is totally different from
those with sigmoidal activation functions or nondecreasing saturated activation functions, which
have been employed extensively in previous multistability papers. By tracking the dynamics of
each state component and applying fixed point theorem and analysis method, some sufficient conditions
are presented to study the multistability and instability, including the total number of
equilibria, their locations, and local stability and instability. The obtained results extend and improve
the very recent works. Two illustrative examples with their simulations are given to verify
the theoretical analysis. |
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| ISSN: | 1085-3375 1687-0409 |