Analysis of two- and three-dimensional fractional-order Hindmarsh-Rose type neuronal models

TL;DR

This paper provides a theoretical stability analysis of fractional-order Hindmarsh-Rose neuronal models and demonstrates rich bursting behaviors through numerical simulations, highlighting the impact of fractional order on system dynamics.

Contribution

It offers the first detailed stability and bifurcation analysis of fractional-order Hindmarsh-Rose models with numerical validation.

Findings

Stability properties depend on fractional order

Hopf bifurcations occur as fractional order varies

Rich bursting behaviors observed in simulations

Abstract

A theoretical analysis of two- and three-dimensional fractional-order Hindmarsh-Rose neuronal models is presented, focusing on stability properties and occurrence of Hopf bifurcations, with respect to the fractional order of the system chosen as bifurcation parameter. With the aim of exemplifying and validating the theoretical results, numerical simulations are also undertaken, which reveal rich bursting behavior in the three-dimensional fractional-order slow-fast system.