Multimode function multistability for Cohen-Grossberg neural networks with mixed time delays

In this paper, we are concerned with the multimode function multistability for Cohen-Grossberg neural networks (CGNNs) with mixed time delays. It is introduced the multimode function multistability as well as its specific mathematical expression, which is a generalization of multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and asymptotic stability. Also, according to the neural network (NN) model and the maximum and minimum values of activation functions, n pairs of upper and lower boundary functions are obtained. Via the locations of the zeros of the n pairs of upper and lower boundary functions, the state space is divided into pni=1(2Hi + 1) parts correspondingly. By virtue of the reduction to absurdity, continuity of function, Brouwer's fixed point theorem and Lyapunov stability theorem, the criteria for multimode function multistability are acquired. Multiple types of multistability, including multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and multiple asymptotic stability, can be achieved by selecting different types of function P(t). Two numerical examples are offered to substantiate the generality of the obtained criteria over the existing results.(c) 2021 ISA. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the multimode function multistability for Cohen-Grossberg neural networks (CGNNs) with mixed time delays, and presents its mathematical expression and criteria. Multiple types of multistability can be achieved by selecting different types of function P(t). The generality of the obtained criteria is substantiated through numerical examples.