Abstract

The main results of this paper are related to studying the dynamics of the Van-der-Pol oscillator, which is under the influence of a driving force and a hysteretic effect, formalized by the Bouc–Wen phenomenological model. The regularizing role of the hysteretic link in the reduction of chaotic regimes is established. The main results are obtained as part of the asymptotic expansion method (small parameter method). A system of two coupled Van-der-Pol oscillators is considered under the conditions of a driving force acting on one of them: the relationship between the amplitudes and frequencies of the natural oscillations of the oscillators is established in an analytical form. The paper also describes a system of cross-related Van-der-Pol oscillators, in which the driving force acting on one of them is determined by the output of a hysteretic transducer, to the input of which the mismatch between the oscillators’ velocities is applied. It is found that the coupling parameter between the oscillators and the parameter that determines the influence of the hysteretic link have a significant effect on the synchronization in the system.

中文翻译：

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滞后相关范德波尔振荡器的动力学：小参数方法

摘要

本文的主要结果与研究 Van-der-Pol 振荡器的动力学有关，该振荡器受驱动力和滞后效应的影响，由 Bouc-Wen 现象学模型形式化。建立了滞后链接在减少混沌状态中的正则化作用。主要结果是作为渐近展开法（小参数法）的一部分获得的。在驱动力作用于其中一个的条件下考虑两个耦合的范德波尔振荡器的系统：以解析形式建立振荡器自然振荡的幅度和频率之间的关系。该论文还描述了一个交叉相关的 Van-der-Pol 振荡器系统，其中作用在其中之一上的驱动力由迟滞传感器的输出决定，振荡器速度之间的失配被应用到其输入。发现振荡器之间的耦合参数和决定滞后链路影响的参数对系统中的同步有显着影响。