Stability and Bifurcation Analysis of a Hindmarsh-Rose Neuronal Model With Time Delay

Abstract

In this research work, we study and analyse Hindmarsh-Rose neuronal system with time delay. Considering the fast sub-system of the model, all the possible non-negative equilibria are obtained and their local as well as global behaviour are studied. Choosing delay as a bifurcation parameter, the existence of the Hopf bifurcation of the system has been investigated. Moreover, we use the Descartes’ sign rule, a powerful tool for real polynomials with constant coefficientsto determine the number of real zeroes of the polynomial function. Classifications of the imaginary roots of the characteristic equation were presented. Some numerical simulations are given to support the analytical results. Some interesting conclusions are obtained from the results obtained at the end of this work.