Multiple exponential stability for short memory fractional impulsive Cohen-Grossberg neural networks with time delays

Abstract

Different from the existing multiple asymptotic stability or multiple Mittag-Leffler stability, the multiple exponential stability with explicit and faster convergence rate is addressed in this paper for short memory fractional-order impulsive Cohen-Grossberg neural networks with time delay. Firstly, ${\prod }_{i=1}^n(2H_i+1)$ total equilibrium points of such n-neuron neural networks can be ensured via the known fixed point theorem. Then, by means of the theory of fractional-order differential equations, the methods of average impulsive interval and Lyapunov function, a series of sufficient conditions for determining the locally exponential stability of ${\prod }_{i=1}^n(H_i+1)$ equilibrium points are obtained based on maximum norm, 1-norm and general q-norm ($q=2^n$), respectively. This paper's research reveals the effects of impulsive function, impulsive interval, fractional order and time delay on the dynamic behaviors. Finally, four examples are proposed to demonstrate the effectiveness of theoretic achievements.