2025/05/28 by Jaume Llibre, Yilei Tang, Llibre, Jaume +5
Mathematics · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2505.21871
openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we obtain the global dynamics and phase portraits of quadratic and cubic quasi-homogeneous but non-homogeneous systems. We first prove that all planar quadratic and cubic quasi-homogeneous but non-homogeneous polynomial systems can be reduced to three homogeneous ones. Then for the homogeneous systems, we employ blow-up method, normal sector method, Poincaré compactification and other techniques to discuss their dynamics. Finally we characterize the global phase portraits of quadratic and cubic quasi-homogeneous but non-homogeneous polynomial systems.