Bifurcation analysis of a fractional-order Pinsky-Rinzel model

TL;DR

This paper investigates a fractional-order Pinsky-Rinzel hippocampal model, analyzing its bifurcation behavior and stability, revealing chaotic dynamics influenced by fractional derivative order and injection currents, with implications for disease control.

Contribution

It introduces a fractional-order version of the Pinsky-Rinzel model and studies its bifurcation and stability properties using numerical methods.

Findings

Chaotic regions depend on fractional derivative order and injection currents.

Bifurcation diagrams reveal complex system behavior.

Numerical stability analysis aids in understanding disease mechanisms.

Abstract

Abstract The present work describes a new fractional-order system of a two-compartment CA3 hippocampal pyramidal cell, which is known as Pinsky-Rinzel model with Caputo fractional derivative. Firstly, The transient of the solutions is investigated. Then based on the bifurcation diagrams, we study the general behavior of the system. In this case, fractional derivative order and currents injection, are taken as bifurcation parameters. Chaotic regions are obtained for different values of the fractional derivative order and different injection currents. Finally, a numerical approach is introduced to study the stability of the system under certain conditions. The obtained results can be considered as help to control relevant diseases caused by maximal injection currents abnormality.