Existence and finite-time stability of discrete fractional-order complex-valued neural networks with time delays

Abstract

Without decomposing complex-valued systems into real-valued systems, the existence and finite-time stability for discrete fractional-order complex-valued neural networks with time delays are discussed in this paper. First of all, in order to obtain the main results, a new discrete Caputo fractional difference equation is proposed in complex field based on the theory of discrete fractional calculus, which generalizes the fractional-order neural networks in the real domain. Additionally, by utilizing Arzela–Ascoli’s theorem, inequality scaling skills and fixed point theorem, some sufficient criteria of delay-dependent are deduced to ensure the existence and finite-time stability of solutions for proposed networks. Finally, the validity and feasibility of the derived theoretical results are indicated by two numerical examples with simulations. Furthermore, we have drawn the following facts: with the lower order, the discrete fractional-order complex-valued neural networks will achieve the finite-time stability more easily.