Analysis of nested repelling mixed-mode oscillations in a slow–fast hard-type van der Pol oscillator subject to weak periodic perturbations

IF 2.6 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physics Letters A Pub Date : 2025-08-04 DOI:10.1016/j.physleta.2025.130861

Naohiko Inaba , Munehisa Sekikawa , Hideaki Okazaki

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引用次数: 0

Abstract

In a previous work (Sekikawa and Inaba, 2025), it was discovered that an unstable canard can be generated by a slow–fast hard-type autonomous van der Pol (vdP) oscillator with fifth-order nonlinearity. In this Letter, we analyze repellers in such a hard-type vdP oscillator when a weak periodic perturbation is applied. We confirm that the repelling oscillations generate successive unnested and nested unstable mixed-mode oscillation-incrementing bifurcations (MMOIBs). According to the numerical results presented here, successive unnested and nested MMOIBs emerge as many times as the system is tracked. The time-series waveforms of the repelling mixed-mode oscillations (MMOs) observed here closely resemble those observed in the case of attracting MMOs, and the bifurcation structures of nested repelling MMOs are also similar to those of the nested attracting MMOs. Nested repelling MMOs represent an entirely novel phenomenon, and we believe that this work could open the path for new research in nonlinear systems.

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弱周期扰动下慢快硬型范德堡尔振荡器的嵌套排斥混合模振荡分析

在先前的工作中（Sekikawa和Inaba， 2025）发现，具有五阶非线性的慢速硬型自主范德波尔（vdP）振荡器可以产生不稳定鸭翼。在这篇文章中，我们分析了在弱周期扰动下这种硬型vdP振荡器中的驱避器。我们证实了排斥振荡产生连续的非嵌套和嵌套不稳定混合模式增振分岔（MMOIBs）。根据本文给出的数值结果，连续的非嵌套和嵌套mmoib在跟踪系统时出现的次数相同。这里观察到的排斥混合模式振荡（MMOs）的时间序列波形与吸引mmo的时间序列波形非常相似，嵌套排斥mmo的分岔结构也与嵌套吸引mmo相似。嵌套排斥mmo代表了一种全新的现象，我们相信这项工作可以为非线性系统的新研究开辟道路。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physics Letters A 物理-物理：综合

CiteScore

5.10

自引率

3.80%

发文量

493

审稿时长

30 days

期刊介绍： Physics Letters A offers an exciting publication outlet for novel and frontier physics. It encourages the submission of new research on: condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. No articles on High Energy and Nuclear Physics are published in Physics Letters A. The journal''s high standard and wide dissemination ensures a broad readership amongst the physics community. Rapid publication times and flexible length restrictions give Physics Letters A the edge over other journals in the field.