1998/01/15 by Alexei D. Kiselev, Kiselev, Alexei D.
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #Optics (physics.optics) #chao-dyn #math-ph #math.MP #nlin.CD #physics.optics
paper · pdf · doi:10.48550/arxiv.physics/9801018
23 pages (LaTeX), 8 figures, uses epsf.sty (submitted to J. of Phys. A)
arxiv created 1998/01/15 · arxiv updated 2009/11/30
The concept of broken symmetry is used to study bifurcations of equilibria and dynamical instabilities in dynamic model of one-mode laser (nonresonant complex Lorenz model) on the basis of modified Hopf theory. It is shown that an invariant set of stationary points bifurcates into an invariant torus (doubly-periodic branching solution). Influence of the symmetry breaking on stability of branching solutions is investigated as a function of detuning. The invariant torus is found to be stable under the detuning exceeds its critical value, so that dynamically broken symmetry results in the apprearance of low-frequency Goldstone-type mode. If the detuning then goes downward and pumping is kept above the threshold, numerical analysis reveals that after a cascade of period-doublings the strange Lorenz attractor is formed at small values of detuning. It is found that there are three types of the system behavior as pumping increases depending on the detuning. Quantum counterpart of the complex Lorenz model is discussed.