Complex bursting oscillations induced by pulse-shaped explosion and integer frequency ratios in a Rayleigh–van der Pol system

IF 1.9 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Pramana Pub Date : 2023-07-17 DOI:10.1007/s12043-023-02566-5

Zhangyao Chen, Xindong Ma, Qinsheng Bi

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引用次数: 0

Abstract

The pulse-shaped explosion (abbreviated as PSE) behavior, represented as the system roots pulse-shaped quantitative changing sharply, is a new way to the bursting oscillations proposed recently. In the present paper, the complex bursting oscillation patterns triggered by the PSE and integer frequency ratios are considered based on a Rayleigh–van der Pol system (abbreviated as RVDPS) excited by the parametrical and external forces. Two cascade bursting oscillations, the cascade supHopf/supHopf bursting oscillations induced by the integer frequency ratios and the cascade supHopf/supHopf bursting oscillations with multiple PSE/PSE hysteresis loops induced by the integer frequency ratios and PSEs, are investigated. We show that the PSEs occur when the system solution curve approaches to infinity at some certain values and the PSEs do not change the stabilities of the attractors. In addition, we find that the frequency and period of the cascade bursting oscillation patterns equal to that of the external force. Our study proposes a new PSE type to the bursting oscillations named the cascade PSEs and increases two cascade bursting oscillation patterns.

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Rayleigh-van - der - Pol系统中脉冲型爆炸和整数频率比引起的复杂爆破振荡

脉冲型爆炸(PSE)行为是近年来提出的一种研究爆炸振荡的新方法，其表现形式为系统根的脉冲型定量急剧变化。本文基于参数力和外力激励下的瑞利-范德波尔系统(简称RVDPS)，研究了由PSE和整数频率比触发的复杂爆破振荡模式。研究了由整数频率比引起的supHopf/supHopf级联爆破振荡和由整数频率比和PSE引起的具有多个PSE/PSE滞回的supHopf/supHopf级联爆破振荡。我们证明了当系统解曲线在某一特定值趋近于无穷时，系统解曲线会发生pse，并且pse不会改变吸引子的稳定性。此外，我们发现叶栅爆破振荡模式的频率和周期与外力的频率和周期相等。本文提出了一种新的爆破振荡PSE类型，即梯级爆破振荡PSE，增加了两种梯级爆破振荡模式。

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

Pramana 物理-物理：综合

CiteScore

3.60

自引率

7.10%

发文量

206

审稿时长

3 months

期刊介绍： Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.