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

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^k equilibrium points with 0≤k≤n, among which 2^k 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.

Keywords: Fractional-order competitive neural networks; Gaussian activation functions; Mittag-Leffler stability; Multistability.