Stability of bifurcating periodic orbits: an application to laser equations

Abstract

Based on the Poincaré-Lindstedt perturbation method, we propose a general analytical procedure to determine the stability of periodic solutions arising from a Hopf bifurcation in dynamical systems. As an application of our method to a physical system, we analyze the stability of bifurcating periodic orbits in a single mode laser. An analytic expression for the associated stability coefficient is obtained and the stability regions are characterized in the space of parameters of this system.