Cascade of torus doubling bifurcations in a detuned laser

Abstract

By using a simplified system of Maxwell—Bloch equations (with the adiabatically excluded polarisation of the medium), we studied the processes proceeding in the cross section of a light wave propagating in a wide-aperture laser emitting at the frequency detuned from the transition-line centre. It is shown that in the model under study the passage to the chaotic regime during a change in the wave propagation velocity across the aperture occurs via the doubling bifurcations of an ergodic two-dimensional torus. The spectrum of Lyapunov exponents is found and it is established that at bifurcation points a structurally unstable three-dimensional torus is produced, which gives rise to a stable doubled ergodic torus.