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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 901519, 20 pages
Research Article

Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions

1Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China
2School of Automation, Southeast University, Nanjing 210096, China
3Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 2 January 2014; Accepted 9 April 2014; Published 6 May 2014

Academic Editor: Weinian Zhang

Copyright © 2014 Xiaobing Nie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.