Dynamic behaviors for inertial neural networks with reaction-diffusion terms and distributed delays

Famei Zheng

doi:10.1186/s13662-021-03330-y

Abstract

A class of inertial neural networks (INNs) with reaction-diffusion terms and distributed delays is studied. The existence and uniqueness of the equilibrium point for the considered system is obtained by topological degree theory, and a sufficient condition is given to guarantee global exponential stability of the equilibrium point. Finally, an example is given to show the effectiveness of the results in this paper.

Highlights

In 1997, Wheeler and Schieve [1] introduced inductance into neural networks and obtained a second-order neural network which is called inertial neural networks (INNs)
Angelaki and Correia [2] studied a model of membrane resonance in pigeon semicircular canal type II hair cells which introduced inertial terms
(i) In this paper, we firstly study a new class of INNs which contains reaction-diffusion terms and distributed delays

Summary

Introduction

In 1997, Wheeler and Schieve [1] introduced inductance into neural networks and obtained a second-order neural network which is called inertial neural networks (INNs). Inertial terms are introduced for biological backgrounds. Angelaki and Correia [2] studied a model of membrane resonance in pigeon semicircular canal type II hair cells which introduced inertial terms. Inertial neural networks (INNs) are represented by second-order differential system. Due to the inertial terms, it is very difficult to study the dynamic properties of the network system. Wang and Jiang [8] considered a class of impulsive INNs with time-varying delays. Winters, and Cheron [9] studied a class of selfselected modular recurrent neural networks with postural and inertial subnetworks

Objectives

Conclusion