Multistability of Fractional-Order Neural Networks With Unbounded Time-Varying Delays

This article addresses the multistability and attraction of fractional-order neural networks (FONNs) with unbounded time-varying delays. Several sufficient conditions are given to ensure the coexistence of equilibrium points (EPs) of FONNs with concave-convex activation functions. Moreover, by exploiting the analytical method and the property of the Mittag-Leffler function, it is shown that the multiple Mittag-Leffler stability of delayed FONNs is derived and the obtained criteria do not depend on differentiable time-varying delays. In particular, the criterion of the Mittag-Leffler stability can be simplified to M-matrix. In addition, the estimation of attraction basin of delayed FONNs is studied, which implies that the extension of attraction basin is independent of the magnitude of delays. Finally, three numerical examples are given to show the validity of the theoretical results.

Automated summary

This article discusses the multistability and attraction of fractional-order neural networks with unbounded time-varying delays. Multiple sufficient conditions are provided for the coexistence of equilibrium points with concave-convex activation functions. The criteria for Mittag-Leffler stability can be simplified to M-matrix and the extension of attraction basin is shown to be independent of the magnitude of delays. Three numerical examples are given to demonstrate the validity of the theoretical results.