School of Mathematical & Statistical Sciences Faculty Publications and Presentations
Global dynamics of cubic Cherkas systems with Z 2 -equivariance (Ⅰ): The saddle case
Document Type
Article
Publication Date
1-2026
Abstract
In this paper, we investigate bifurcation diagrams and global phase portraits on the Poincaré disc for a cubic Cherkas system with symmetry. When the sum of indices of equilibria is −1, we obtain some interesting dynamical behaviors, including Hopf bifurcation, heteroclinic bifurcation, saddle-node bifurcation, and saddle connection bifurcation. These results greatly enrich the dynamics of planar nonlinear differential systems and demonstrate different features.
Recommended Citation
Chen, Hebai, Dehong Dai, Zhaosheng Feng, and Rui Zhang. "Global dynamics of cubic Cherkas systems with $\mathbb {Z} _2 $-equivariance (Ⅰ): The saddle case." Discrete and Continuous Dynamical Systems 46 (2026): 209-237. https://doi.org/10.3934/dcds.2025097
Publication Title
Discrete and Continuous Dynamical Systems
DOI
10.3934/dcds.2025097
