Global Mittag-Leffler stability and existence of the solution for fractional-order complex-valued NNs with asynchronous time delays.
Journal:
Chaos (Woodbury, N.Y.)
Published Date:
Nov 1, 2021
Abstract
This paper is dedicated to exploring the global Mittag-Leffler stability of fractional-order complex-valued (CV) neural networks (NNs) with asynchronous time delays, which generates exponential stability of integer-order (IO) CVNNs. Here, asynchronous time delays mean that there are different time delays in different nodes. Two new inequalities concerning the product of two Mittag-Leffler functions and one novel lemma on a fractional derivative of the product of two functions are given with a rigorous theoretical proof. By utilizing three norms, several novel conditions are concluded to guarantee the global Mittag-Leffler stability and the existence and uniqueness of an equilibrium point. Considering the symbols of the matrix elements, the properties of an M-matrix are extended to the general cases, which introduces the excitatory and inhibitory impacts on neurons. Compared with IOCVNNs, exponential stability is the special case of our results, which means that our model and results are general. At last, two numerical experiments are carried out to explain the theoretical analysis.