Multistability and instability of competitive neural networks with Mexican-hat-type activation functions
type: Item
instance of: scholarly article
title: Multistability and instability of competitive neural networks with Mexican-hat-type activation functions
zbMATH Open document ID: 1474.34358
DOI: 10.1155/2014/901519
author: Xiaobing Nie
author: Jinde Cao
author: Shumin Fei
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 92B20
zbMATH DE Number: 7023273
Wikidata QID: Q59042717
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/901519
OpenAlex ID: W1999893907
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description: scientific article; zbMATH DE number 7023273