Multistability of delayed fractional-order competitive neural networks

This paper is concerned with the multistability of fractional-order competitive neural networks (FCNNs) with time-varying delays. Based on the division of state space, the equilibrium points (EPs) of FCNNs are given. Several sufficient conditions and criteria are proposed to ascertain the multiple O(t(-alpha))-stability of delayed FCNNs. The O(t(-alpha))-stability is the extension of Mittag-Leffler stability of fractional-order neural networks, which contains monostability and multistability. Moreover, the attraction basins of the stable EPs of FCNNs are estimated, which shows the attraction basins of the stable EPs can be larger than the divided subsets. These conditions and criteria supplement and improve the previous results. Finally, the results are illustrated by the simulation examples. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the multistability of fractional-order competitive neural networks with time-varying delays. The equilibrium points of the networks are given by division of state space, and several sufficient conditions and criteria are proposed to ascertain the multiple stability of the networks. Additionally, the attraction basins of the stable equilibrium points are estimated, showing that they can be larger than the divided subsets.