THERMAL SCIENCE

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Fengxia Wu

,

Zitian Li

BIFURCATION CHARACTERISTICS AND BURSTING OSCILLATION OF DUFFING-VAN DER POL OSCILLATOR

ABSTRACT
In this paper, we study the bifurcation characteristics and bursting oscillation of the Duffing-Van der Pol system with periodic excitation. Due to the different frequency scales between the excitation frequency and the natural frequency in the oscillator, when the periodic excitation changes slowly with time, the system is considered as a slow subsystem, and when it is fixed, the system is considered as a fast subsystem. We analyze the bifurcation characteristics of the fast subsystem and use the slowly varying parameter as the bifurcation parameter to show how the bursting oscillations are generated. Furthermore, the phase diagram and time-history diagram of fold-fold bursting oscillation, fold-subHopf bursting oscillation, supHopf-supHopf bursting oscillation, and homoclinic-homoclinic bursting oscillation are given by numerical simulation. Combined with the fig-ures, it is found that these four kinds of bursting oscillations with bifurcation delay phenomenon are symmetrical and further reveal the bifurcation mechanisms of these four kinds of bursting oscillations.
KEYWORDS
fast-slow dynamics, fold bifurcation, homoclinic bifurcation, Hopf bifurcation
PAPER SUBMITTED: 2023-12-25
PAPER REVISED: 2024-07-06
PAPER ACCEPTED: 2024-07-06
PUBLISHED ONLINE: 2025-07-06
DOI REFERENCE: https://doi.org/10.2298/TSCI2503849W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 3, PAGES [1849 - 1859]
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Bifurcation characteristics and bursting oscillation of Duffing-Van der Pol oscillator

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence