Stability and Hopf Bifurcation in a Modified Sprott C System

Abstract

In this article, a Modifed Sprott $C$ system is considered. The stability of equilibrium points and the occurrence of Hopf bifurcation of the system are investigated. It was proven that the system displays a Hopf bifurcation at α=0. In addition, by applying normal form theory, the stability, direction and increase (decrease) of the period of bifurcating periodic solutions of the system are illustrated. It was 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 bifurcating periodic solutions increases.