Yuhuan Lu, Rui Zhang
Abstract:
In this article, we study a modified hybrid Van der Pol-Rayleigh oscillator.
We consider bifurcation diagrams and global phase portraits in the Poincare disc
under some restrictions on the parameters.
The resulting bifurcation diagram is complex, containing one saddle-node
bifurcation surface at infinity, one cusp bifurcation surface,
one Hopf bifurcation surface, and two generalized heteroclinic bifurcation surfaces.
Submitted December 22, 2025. Published March 31, 2026.
Math Subject Classifications: 34C07, 34C15, 37G15.
Key Words: Van der Pol-Rayleigh oscillator; bifurcation; phase portrait; limit cycle.
DOI: 10.58997/ejde.2026.25
Show me the PDF file (1637 KB), TEX file for this article.
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Yuhuan Lu School of Mathematics and Statistics MNP-LAMA, Central South University Changsha, Hunan 410083, China email: lu_yuhuan@csu.edu.cn |
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Rui Zhang School of Mathematics and Statistics MNP-LAMA, Central South University Changsha, Hunan 410083, China email: zhang_rui@csu.edu.cn |
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