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arXiv · 2511.01922

The discontinuous limit case of an archetypal oscillator with constant excitation and van der Pol damping: A single equilibrium

Xiuli Cen·Hebai Chen·Yilei Tang·Zhaoxia Wang
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Abstract

This paper investigates the global dynamics of the discontinuous limit case of an archetypal oscillator with constant excitation that exhibits a single equilibrium. For parameter regions in which this oscillator possesses two or three equilibria, the global bifurcation diagram and the corresponding phase portraits on the Poincare disc have been presented in [Phys. D, 438 (2022) 133362]. The present work completes the global structure of the discontinuous limit case of an archetypal oscillator with constant excitation. Although the dynamical phenomena are less rich compared to systems with more than one equilibrium, the presence of a single equilibrium gives rise to additional limit cycles surrounding it, thereby enriching the overall dynamics and making the analysis substantially more intricate than in the previously studied cases.

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Xiuli Cen, Hebai Chen, Yilei Tang, Zhaoxia Wang. 2025-11-02. The discontinuous limit case of an archetypal oscillator with constant excitation and van der Pol damping: A single equilibrium. https://arxiv.org/abs/2511.01922

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