单模激光Haken-Lorenz系统的振荡解析解(英文)

An Oscillation Analytic Solution for Single-Mode Laser Haken-Lorenz System

研究了单模激光Haken-Lorenz系统在Hopf分歧点处的动力学行为.求出了Haken-Lorenz系统的定态解,采用线性稳定性原理对定态解进行了稳定性分析,获得了本征值方程,进而确定了系统的Hopf分歧点μc.利用级数法求出了系统在分歧点处的时间周期振荡解的解析表达式.通过计算机对系统分歧点处的动力学行为进行了数值模拟,结果表明,系统在分歧点处存在一个极限环,即时间周期振荡解.与理论分析的解析结果相一致.

Dynamical behaviours of a single-mode laser Haken-Lorenz system were investigated. The steady state solution of the system was obtained. Stability analysis was given by using the principle of linear stability. Characteristic equation was gotten and Hopf bifurcation pointμc was determined. A periodic oscillation analytic solution for the system at bifurcation point was obtained by using the method of series. The dynamical behaviors of the system were given by computer numerical simulation. The results show that when the bifurcation parameter μ crosses the critical value μc and Haken-Lorenz system gives rise to limit cycle, i. e. periodic oscillation solution,the result accords with the analytic one.