Multistability of Competitive Neural Networks with Non-monotonic Piecewise Linear Activation Functions

NIE Xiao-Bing; CAO Jin-De; FEI Shu-Min

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Multistability of Competitive Neural Networks with Non-monotonic Piecewise Linear Activation Functions

NIE Xiao-Bing 1 *, CAO Jin-De 2, FEI Shu-Min 3

1. Department of Mathematics, Southeast University, Nanjing 210096;School of Automation, Southeast University, Nanjing 210096

2. Department of Mathematics, Southeast University, Nanjing 210096

3.School of Automation, Southeast University, Nanjing 210096

*Correspondence author

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Funding: Specialized Research Foundation for the Doctoral Program of HigherEducation （No.20120092120029）, National Natural Science Foundation of China （No.61203300）

Opened online: 6 June 2016

Accepted by: none

Citation: NIE Xiao-Bing, CAO Jin-De, FEI Shu-Min.Multistability of Competitive Neural Networks with Non-monotonic Piecewise Linear Activation Functions[OL]. [ 6 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4693708

This paper addresses the issue of multistability for competitive neural networks. First, a general class of continuous non-monotonic piecewise linear activation functions is introduced. Then, based on the fixed point theorem, the contraction mapping theorem and the eigenvalue properties of strict diagonal dominance matrix, it is shown that under some conditions, such $n$-neuron competitive neural networks have exactly $5^n$ equilibrium points, among which $3^n$ equilibrium points are locally exponentially stable. Moreover, it is revealed that the neural networks with non-monotonic piecewise linear activation functions introduced in this paper can have greater storage capacity than the ones with Mexican-hat-type activation function.

Keywords:Competitive neural networks, Multistability, Non-monotonic piecewise linear activation functions.

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