Dynamical behaviors of a van der Pol-Duffing oscillator with indefinite degree

Communications on Pure &amp Applied Analysis 2026 Open access

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Authors: Hebai Chen, Zhaosheng Feng, Zhijie Li, Zhaoxia Wang
DOI: 10.3934/cpaa.2026027
Cited by: 1
References: 19

Abstract

In this paper, we study a van der Pol-Duffing oscillator with indefinite degree in the Poincaré disc. Some fascinating and rich dynamics are presented, including abundant nonlinear phenomena such as limit cycles, figure-eight loops, and saddle connections, thereby providing the complete global structure.

Fields of Study & Subjects

Chaos control and synchronization Advanced Differential Equations and Dynamical Systems Advanced Differential Geometry Research

Publication details

Journal / source
Communications on Pure &amp Applied Analysis
Publisher
American Institute of Mathematical Sciences (AIMS)
Volume
30
Issue
0
Pages
21–60
Publication date
1 January 2026