2017/08/11 by Yilei Tang, Tang, Yilei
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1708.03444
openalex publication_date 2017/08/11 · openalex created_date 2017/08/31 · openalex updated_date 2026/07/28
In this paper we research global dynamics and bifurcations of planar piecewise smooth quadratic quasi--homogeneous but non-homogeneous polynomial differential systems. We present sufficient and necessary conditions for the existence of a center in piecewise smooth quadratic quasi--homogeneous systems. Moreover, the center is global and non-isochronous if it exists, which cannot appear in smooth quadratic quasi-homogeneous systems. Then the global structures of piecewise smooth quadratic quasi--homogeneous but non-homogeneous systems are studied. Finally we investigate limit cycle bifurcations of the piecewise smooth quadratic quasi-homogeneous center and give the maximal number of limit cycles bifurcating from the periodic orbits of the center by applying the Melnikov method for piecewise smooth near-Hamiltonian systems.