非线性增益下半导体激光方程的动力学行为分析
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国家自然科学资金项目(20476041,10602020)


Dynamical analysis on the semiconductor lasers with nonlinear gain saturation coefficient
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    摘要:

    分析了在非线性增益下各种因素对Lang-Kobayashi模型动力学行为的影响.由于时滞反馈的作用,系统中存在着不同的ECM 解,Hopf分岔是这些ECM 解失稳的主要原因,进而演化为各种形式的混沌解,不同吸引子之间的相互作用会引发混沌结构的突变,表现为混沌吸引子在空间尺寸上的明显变化,随着时滞量的变化,这些演化模式会重复出现.值得指出的是,在一定条件下,不同频率的两个 ECM共存,其中之一会由Hopf分岔失稳,并由倍周期分岔进入混沌,最终通过混沌危机回到另一个稳定的ECM上.另外,随着非线性增益系数的变化,在极坐标下系统的概周期运动的两个频率相差很大,激光器呈现出明显的快慢效应.

    Abstract:

    The influence of various factors on the dynamics of the Lang-Kobayash equations with nonlinear gain saturation coefficient was investigated. Because of the existence of time delay feedback, there may exist different ECM solutions, which may lose the stabilities via Hopf bifurcation and further evolve to various forms of chaos. The interactions between different attractors may cause the catastrophe of chaotic structures, which results in sudden space scale change of chaos. With the change of time delay, these modes will appear again and again. It is worth to point out that, for certain parameter conditions, two ECM solutions with different frequencies may coexist, one of which may lose the stability via Hopf bifurcation and leads to chaos by cascading of perioddoubling bifurcations, while it may finally settle down to the other ECM solution via chaos crisis. Furthermore, with the variation of nonlinear gain saturation coefficient, the two frequencies of the quasiperiodic movement in polar coordinate are quite separated, which results in the obvious fastslow effect in the lasers.

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王作雷,毕勤胜.非线性增益下半导体激光方程的动力学行为分析[J].动力学与控制学报,2008,6(2):102~106; Wang Zuolei, Bi Qinsheng. Dynamical analysis on the semiconductor lasers with nonlinear gain saturation coefficient[J]. Journal of Dynamics and Control,2008,6(2):102-106.

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  • 收稿日期:2008-02-24
  • 最后修改日期:2008-03-10
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