A fractional order model of electrically coupled neurons & studying the stability of this model

Abstract

This paper discusses the stability of equilibrium points in coupled fractional oscillators. Coupled fractional oscillators are often used to model biological phenomena such as the flow of ions in two linked neurons via electrical coupling. In conjunction, the paper shows the equilibrium points and their asymptotic stability conditions. Simulations demonstrate the main differences between the integer model and the fractional order model based on stability. We conclude that the stability of coupled fractional oscillators is as stable as its integer of order one. © 2008 Springer-Verlag.