Hopf bifurcation analysis in the [formula omitted] system

Abstract

In this paper, a three dimensional autonomous nonlinear system called the T system which has potential application in secure communications is considered. By choosing an appropriate bifurcation parameter, we prove that the T system displays a Hopf bifurcation under certain conditions. By applying normal form theory, the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are presented. Finally, a numerical example is given to support the analytic results.