Open AccessLimit cycles and global dynamic of planar cubic semi-quasi-homogeneous systems
Author(s) -
Zecen He,
Haihua Liang,
Xiang Zhang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021049
Subject(s) - limit cycle , homogeneous , limit (mathematics) , planar , phase portrait , mathematics , cubic crystal system , mathematical analysis , physics , combinatorics , computer science , condensed matter physics , quantum mechanics , bifurcation , computer graphics (images) , nonlinear system
Denote by CH, CSH, CQH, and CSQH the planar cubic homogeneous, cubic semi-homogeneous, cubic quasi-homogeneous and cubic semi-quasi-homogeneous differential systems, respectively. The problems on limit cycles and global dynamics of these systems have been solved for CH, and partially for CSH. This paper studies the same problems for CQH and CSQH. We prove that CQH have no limit cycles and CSQH can have at most one limit cycle with the limit cycle realizable. Moreover, we classify all the global phase portraits of CSQH.