Solution of the system of Lorenz equations in the asymptotic limit of large Rayleigh numbers I

A quantum Fokker–Planck equation is derived for a model system of a single-mode laser based on two-level atoms with dynamics of the trajectories described by the nonlinear differential Lorenz system. The trajectories are investigated in the asymptotic limit of strong pumping, or large Rayleigh number, in the region of applicability of averaging methods. Two bifurcations that arise when the damping constant of the field is varied are described: the appearance of limit cycles and Hopf inverse bifurcation.