Multiple Mittag-Leffler stability of fractional-order competitive neural networks with Gaussian activation functions.

Journal: Neural networks : the official journal of the International Neural Network Society
Published Date: Sep 21, 2018

Abstract

In this paper, we explore the coexistence and dynamical behaviors of multiple equilibrium points for fractional-order competitive neural networks with Gaussian activation functions. By virtue of the geometrical properties of activation functions, the fixed point theorem and the theory of fractional-order differential equation, some sufficient conditions are established to guarantee that such n-neuron neural networks have exactly 3 equilibrium points with 0≤k≤n, among which 2 equilibrium points are locally Mittag-Leffler stable. The obtained results cover both multistability and mono-stability of fractional-order neural networks and integer-order neural networks. Two illustrative examples with their computer simulations are presented to verify the theoretical analysis.

Authors

  • Pingping Liu
    The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of Mathematics, Southeast University, Nanjing 211189, China. Electronic address: pingpingliu@seu.edu.cn.
  • Xiaobing Nie
    Department of Mathematics, Southeast University, Nanjing 210096, China; School of Computing, Engineering and Mathematics, University of Western Sydney, Sydney NSW 2751, Australia. Electronic address: xbnie@seu.edu.cn.
  • Jinling Liang
    Department of Mathematics, Southeast University, Nanjing 210096, China; CSN Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Electronic address: jinlliang@seu.edu.cn.
  • Jinde Cao

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