Van der Pol and Rayleigh oscillators are two traditional paradigms of nonlinear dynamics. They can be subsumed into a general form of Liénard–Levinson–Smith(LLS) system. Based on a recipe for finding out maximum number of limit cycles possible for a class of LLS oscillator, we propose here a scheme for systematic designing of generalised Rayleigh and Van der Pol families of oscillators with a desired number of multiple limit cycles. Numerical simulations are explicitly carried out for systematic search of the parameter space for bi-rhythmic and tri-rhythmic systems and their higher order variants.

中文翻译：

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Van der Pol和Rayleigh振荡器族的双节奏和三节奏模型的系统设计

Van der Pol和Rayleigh振荡器是非线性动力学的两个传统范例。它们可以归纳为Liénard–Levinson–Smith（LLS）系统的一般形式。基于找出一类LLS振荡器可能的最大极限周期数的方法，我们在此提出一种系统设计方案，用于系统设计具有所需数量的多个极限周期的广义瑞利和范德波尔振荡器系列。明确地进行了数值模拟，以便系统搜索双节奏和三节奏系统及其更高阶变体的参数空间。