Stability and Hopf Bifurcation in a Modified Sprott C System

Abstract

In this article, a Modified Sprott C system is considered. The stability of equilibrium points and the occurrence of Hopf bifurcation in the system are investigated. It has been proved that the system displays a Hopf bifurcation at α = 0. Additionally, by applying normal form theory, the stability, direction and increase (or decrease) of the period of bifurcating periodic solutions of the system are illustrated. It has been shown that the solutions of bifurcating periodic solutions at the bifurcation value α = 0 are unstable. The type of Hopf bifurcation is subcritical and the periods of the bifurcating periodic solutions increase.