Global Mittag-Leffler stability analysis of impulsive fractional-order complex-valued BAM neural networks with time varying delays

摘要

This paper investigates the stability of impulsive fractional-order complex-valued BAM neural networks with time varying delays. As the extension of fractional-order real-valued BAM neural networks, fractional-order complex-valued BAM neural networks have complex-valued states, synaptic weights, and the activation functions. Two different kinds of activation functions are considered, along with popular bounded and Lipschitz-kind activation functions. By using Lyapunov function and Homomorphic mapping theorem, sufficient conditions for the existence of unique equilibrium and global asymptotic stability of complex-valued systems are derived. In derivation we separated nonlinear complex-valued activation functions into real and imaginary parts. Moreover, Mittag-Leffler stability for BAM neural networks(BAMNNs) have been proposed when the nonlinear complex activation functions are bounded. Simulation results are presented to prove the efficiency of the obtained methods. (C) 2019 Elsevier B.V. All rights reserved.