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

6-2025

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.

Publication Title

Discrete and Continuous Dynamical Systems

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