Hopf Bifurcation and Global Dynamics Analysis of Generalized Sprott L System

Abstract

A simple chaotic system with only one nonlinearity and five terms was introduced by Sprott. We consider the generalized Sprott differential system. We study the local stability of equilibrium points and local bifurcation, in particular, by choosing an appropriate bifurcation parameter, the paper proves that Hopf bifurcation occur in the system, and presented a formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solution by applying normal form theory. Moreover, we study the dynamics near and at infinity by using the Poincar´e compactification to describe the global dynamics of the trajectories of the system. Our results show that the real parameters do not affect the global dynamics at infinity of the system.

Keywords

• generalized sprott l system; hopf bifurcation; poincare compactification; dynamics at infinity