Homoclinical structure of SICNNs with rectangular input currents

TL;DR

This paper investigates the complex dynamics of SICNNs with various inputs, demonstrating the existence of homoclinic and heteroclinic motions and their relation to quasi-periodic outputs, enhancing understanding of neural network behavior.

Contribution

It provides a functional description of homoclinic and heteroclinic motions in SICNNs with continuous and discontinuous inputs, revealing their dynamic properties.

Findings

Existence of homoclinic and heteroclinic motions in SICNNs.

Networks exhibit motions asymptotic to quasi-periodic outputs.

Demonstration of complex dynamic behaviors in neural networks.

Abstract

Shunting inhibitory cellular neural networks (SICNNs) with continuous as well as discontinuous external inputs are investigated. The descriptions of homoclinic and heteroclinic motions are provided in the functional sense for the multidimensional dynamics of SICNNs, and it is demonstrated that the networks under investigation exhibit such motions. Homoclinic and heteroclinic outputs that are asymptotic to quasi-periodic outputs are illustrated.