Non-resonant double Hopf bifurcation of a class-B laser system

Abstract

We investigate the double Hopf bifurcation at positive equilibrium point of a class-B laser system. Firstly, we give the critical values of Hopf and double Hopf bifurcations. Secondly, we implement the normal form method and the center manifold theory for a class-B laser system, and derive the universal unfolding of the double Hopf bifurcation. Thirdly, some dynamic behaviors, such as periodic and quasi-periodic solutions, are observed using numerical simulation.