Exact coexistence and locally asymptotic stability of multiple equilibria for fractional-order delayed Hopfield neural networks with Gaussian activation function

This paper explores the multistability issue for fractional-order Hopfield neural networks with Gaussian activation function and multiple time delays. First, several sufficient criteria are presented for ensuring the exact coexistence of 3(n) equilibria, based on the geometric characteristics of Gaussian function, the fixed point theorem and the contraction mapping principle. Then, different from the existing methods used in the multistability analysis of fractional-order neural networks without time delays, it is shown that 2(n) of 3(n) total equilibria are locally asymptotically stable, by applying the theory of fractional-order linear delayed system and constructing suitable Lyapunov function. The obtained results improve and extend some existing multistability works for classical integer-order neural networks and fractionalorder neural networks without time delays. Finally, an illustrative example with comprehensive computer simulations is given to demonstrate the theoretical results. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the multistability issue of fractional-order Hopfield neural networks with Gaussian activation function and multiple time delays. The study presents criteria for ensuring the existence of 3(n) equilibria, and shows that 2(n) of them are locally asymptotically stable. The results extend existing works on multistability in integer-order and fractional-order neural networks.