GLOBAL DYNAMICS AND BIFURCATION OF PLANAR PIECEWISE SMOOTH QUADRATIC QUASI-HOMOGENEOUS DIFFERENTIAL SYSTEMS

被引：3
|
作者：
Tang, Yilei [1 ,2 ]
机构：
[1] Shanghai Jiao Tong Univ, Sch Math Sci, Dongchuan Rd 800, Shanghai 200240, Peoples R China
[2] Univ Maribor, Ctr Appl Math & Theoret Phys, Krekova 2, SI-2000 Maribor, Slovenia
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 04期
基金：
欧盟地平线“2020”; 中国国家自然科学基金;
关键词：
Quasi-homogeneous polynomial systems; global phase portrait; bifurcation of piecewise system; Melnikov function; 1ST INTEGRALS; LIMIT-CYCLES; INTEGRABILITY; EQUATIONS; CENTERS;
D O I：
10.3934/dcds.2018082
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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, which cannot appear in smooth quadratic quasi-homogeneous systems. Then the global structures of piecewise smooth quadratic quasi-homogeneous but non-homogeneous systems are obtained. Finally we investigate limit cycle bifurcations of the piecewise quadratic quasi-homogeneous center and give the maximal number of limit cycles bifurcating from periodic orbits of the center by applying the Melnikov method for piecewise smooth near-Hamiltonian systems.
引用
收藏
页码：2029 / 2046
页数：18
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