Hopf bifurcation analysis in the TT system

In this paper, a three dimensional autonomous nonlinear system called the TT system which has potential application in secure communications is considered. By choosing an appropriate bifurcation parameter, we prove that the TT 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.