Hopf bifurcation analysis in the system

Abstract: In this paper, a three dimensional autonomous nonlinear system called the system which has potential application in secure communications is considered. By choosing an appropriate bifurcation parameter, we prove that the 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. [Copyright &y& Elsevier]