Multiple Mittag–Leffler Stability of Fractional-Order Recurrent Neural Networks

In this paper, coexistence and stability of multiple equilibrium points of fractional-order recurrent neural networks are addressed. Several sufficient conditions are derived for ascertaining the existence of Πi=1n(2Ki+ 1) equilibrium points (Ki≥ 0) and the local Mittage - Leffler stability Πi=1n(Ki+ 1) equilibrium points of them by using the geometrical properties of activation functions and algebraic properties of nonsingular M-matrix. In contrast with many existing results, the derived results cover both mono-stability and multistability, and the activation functions herein could be nonmonotonic and nonlinear in any open interval. In addition, three numerical examples are elaborated to substantiate the efficacy and characteristics of the theoretical results.