Stability of discrete‐time fractional‐order time‐delayed neural networks in complex field

Abstract

Dynamics of discrete‐time neural networks have not been well documented yet in fractional‐order cases, which is the first time documented in this manuscript. This manuscript is mainly considered on the stability criterion of discrete‐time fractional‐order complex‐valued neural networks with time delays. When the fractional‐order β holds 1 < β < 2, sufficient criteria based on a discrete version of generalized Gronwall inequality and rising function property are established for ensuring the finite stability of addressing fractional‐order discrete‐time‐delayed complex‐valued neural networks (FODCVNNs). In the meanwhile, when the fractional‐order β holds 0 < β < 1, a global Mittag–Leffler stability criterion of a class of FODCVNNs is demonstrated with two classes of neuron activation function by means of two different new inequalities, fractional‐order discrete‐time Lyapunov method, discrete version Laplace transforms as well as a discrete version of Mittag–Leffler function. Finally, computer simulations of two numerical examples are illustrated to the correctness and effectiveness of the presented stability results.