We revisit the model of the laser with feedback and the minimal nonlinearity leading to chaos. Although the model has its origin in laser physics, with peculiarities related to the CO2 laser, it belongs to the class of the three-dimensional paradigmatic nonlinear oscillator models giving chaos. The proposed model contains three key nonlinearities, two of which are of the type xy, where x and y are the fast and slow variables. The third one is of the type xz2, where z is an intermediate feedback variable. We analytically demonstrate that it is essential for producing chaos via local or global homoclinic bifurcations. Its electronic implementation in the range of kilo Hertz region confirms its potential in describing phenomena evolving on different time scales.

中文翻译：

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带反馈的激光混沌最小通用模型

我们重新审视了具有反馈和导致混沌的最小非线性的激光器模型。尽管该模型起源于激光物理学，但具有与一氧化碳2激光，属于给出混沌的三维范式非线性振荡器模型类。所提出的模型包含三个关键非线性，其中两个属于X是的， 在哪里X和是的是快变量和慢变量。第三个是类型Xz2， 在哪里z是一个中间反馈变量。我们通过分析证明，通过局部或全局同宿分岔产生混沌是必不可少的。它在千赫兹范围内的电子实现证实了它在描述在不同时间尺度上演变的现象方面的潜力。