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. Highlights • FOCNNs with Gaussian activation functions are introduced. • Coexistence and local stability of multiple equilibrium points are investigated. • n -neuron networks have exactly 3 k equilibrium points with 0 ≤ k ≤ n. • 2 k equilibrium points are locally Mittag-Leffler stable. • The obtained results cover both multistability and mono-stability. [ABSTRACT FROM AUTHOR]