Chaotic Dynamics Of Lorenz-Haken Equation And Its Application In Network

Considering the atomic coherences and injected classical field, we derived the non-phase-locking Lorenz-Haken equation by using the technique of stochastic differential equations. The effects of detuning, injected field and the atomic coherence on the dynamical characteristics of this equation is then numerically studied. The results show that in laser working situations, the detuning results in the chaotic behaviors of the light phase. Under different conditions, the system can generate four attractors, double attractors and single attractor, and the fractal dimension of the system is larger than the locking-phase system. The optical detuning, injected field and atomic coherence can inhibit the chaos of cavity field. In the optical bistability regions, we get symmetric bistability pair, but never find the chaotic attractors.Next, the dynamics of an ensemble of two-level atoms injected into a single-mode cavity is studied in the exact atom-field interaction situation, in which the counter-rotating terms, which describe the so called virtual photon processes, neglected in the rotating-wave approximation are considered. The cavity mode is driven by the injected classical field, and the atom is prepared in a coherent superposition of the two levels. We numerically study the dynamics of this equation. We find that the virtual photon processes have strong effects on the dynamics, which can cause the trajectory in phase space of strange attractor spiral around four focus points, and the trajectory is modulated by virtual photon processes. The chaos region in parameter space is now increased. It should be stressed that the strange attractor can exist in optical bistability, and if the atomic coherences and classical field can inhibit chaos depending the laser frequency.Last, dynamics behavior of the arrays of coupled Lorenz oscillators in cobweb geometries are studied numerically. The center-driver oscillator can promote the synchronization of the ring, and the coupled ring can also decrease the critical value of the longitudinal coupled coefficient to reach the transverse synchronization.