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首页> 外文期刊>Journal of Experimental and Theoretical Physics >Complex dynamics and chaos in the parametric coupling of counter-propagating waves
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Complex dynamics and chaos in the parametric coupling of counter-propagating waves

机译：对向传播波的参数耦合中的复杂动力学和混沌

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摘要

We study the dynamics of a distributed self-oscillating system of three parametrically coupled waves, one of which is propagating counter to the other two. We show that an infinite number of natural modes are self-excited as the bifurcation parameter, which has the meaning of the pump amplitude, increases without bound. Exact solutions describing steady-state oscillation regimes are found. We present the results of computer simulation, which show that for moderate pump amplitudes the transient process terminates when a stationary state corresponding to the fundamental mode sets in. As supercritically increases, the oscillations become chaotic, with the transition to chaos being rapid. We note an analogy that exists between the dynamics of such a system and the dynamics of a Lorentz system.
机译：我们研究了三个参数耦合波的分布式自振荡系统的动力学，其中一个正与另外两个相反。我们显示出无限自然模式是自激的，因为分叉参数（具有泵幅度的含义）无限制地增加。找到描述稳态振荡状态的精确解。我们提供了计算机仿真的结果，该结果表明，对于中等幅度的泵浦，当对应于基本模式的稳态进入时，瞬态过程终止。随着超临界值的增加，振荡变得混乱，并迅速转变为混沌。我们注意到这种系统的动力学与洛伦兹系统的动力学之间存在类比。

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