In this paper, the phase-portraits of plane homogeneous polynomial vector fields are studied and some formulae for the calculation of the number of different global phase-portraits of plane homogeneous polynomial vect...In this paper, the phase-portraits of plane homogeneous polynomial vector fields are studied and some formulae for the calculation of the number of different global phase-portraits of plane homogeneous polynomial vector fields are given. Some necessary and sufficient conditions for the global stability of these vector fields are derived.展开更多
This article analyses a non-Lienard type planar cubic system, and a complete qualitative analysis is given for the system, especially the conclusions for the non-existence, existence and uniqueness of limit cycles are...This article analyses a non-Lienard type planar cubic system, and a complete qualitative analysis is given for the system, especially the conclusions for the non-existence, existence and uniqueness of limit cycles are obtained.展开更多
In this paper,we use the canonical forms of homogeneous polynomials of degree 3 to study the global properties of cubic systems =x+P<sub>3</sub>（x,y）,=y+Q<sub>3</sub>（x,y）（0.1） where P<...In this paper,we use the canonical forms of homogeneous polynomials of degree 3 to study the global properties of cubic systems =x+P<sub>3</sub>（x,y）,=y+Q<sub>3</sub>（x,y）（0.1） where P<sub>3</sub> and Q<sub>3</sub> are homogeneous polynomials of degree 3 in x,y.Through this work,we draw an overall outline of such systems.展开更多
文摘In this paper, the phase-portraits of plane homogeneous polynomial vector fields are studied and some formulae for the calculation of the number of different global phase-portraits of plane homogeneous polynomial vector fields are given. Some necessary and sufficient conditions for the global stability of these vector fields are derived.
文摘This article analyses a non-Lienard type planar cubic system, and a complete qualitative analysis is given for the system, especially the conclusions for the non-existence, existence and uniqueness of limit cycles are obtained.
基金Supported by the National Natural Science Foundation of China,No.19371069
文摘In this paper,we use the canonical forms of homogeneous polynomials of degree 3 to study the global properties of cubic systems =x+P<sub>3</sub>（x,y）,=y+Q<sub>3</sub>（x,y）（0.1） where P<sub>3</sub> and Q<sub>3</sub> are homogeneous polynomials of degree 3 in x,y.Through this work,we draw an overall outline of such systems.
