Stability analysis and synchronization of incommensurate fractional-order neural netwroks

Amel Hioual,Taki Eddine Oussaeif

doi:10.55059/ijm.2022.1.1/7

Abstract

This paper develops a theoretical framework for analyzing the stability of nonlinear incommensurate fractional- order neural networks. A necessary theorem for asymptotical stability is established using the characteristic equation for a nonlinear fractional-order system, and how to employ this theorem in stabilization is also presented. With the suitable control, the difficulties of stabilization and synchronization of fractional-order chaotic incommensurate fractional-order neural networks may be readily overcome. Two numerical examples have been shown to demonstrate how the established theory may be used to investigate stability and construct stabilization controllers.

Highlights

The study of differential and integral operators of real and complex order referred to as fractional calculus was developped by many famous mathematicians such as Liouville, Riemann, Abel, and CaputoEven though the branch of fractional calculus began practically concurrently with its integer-order equivalent, the mathematics and, in particular, its applications are somewhat less developed, and several causes have led to this conclusion
The stability of incommensurate fractional-order neural networks is investigated in this research
Several interesting stability criteria are obtained from the introduced characteristic equation

Summary

Introduction

The study of differential and integral operators of real and complex order referred to as fractional calculus was developped by many famous mathematicians such as Liouville, Riemann, Abel, and CaputoEven though the branch of fractional calculus began practically concurrently with its integer-order equivalent, the mathematics and, in particular, its applications are somewhat less developed, and several causes have led to this conclusion. Neural networks have received a great deal of attention due to their effective applications in a wide range of fields, including optimization, function approximation, associative memory, signal processing, automated control, and etc [7][24][22]. These applications rely significantly on the stability qualities of neural networks.

Preliminaries

Mains results

Stability of incommensurate fractional-order neural netwroks

Synchronization of incommensurate fractional order neural networks

Numerical examples

Conclusion