# LIMIT CYCLES FOR PLANAR SEMI-QUASI-HOMOGENEOUS POLYNOMIAL VECTOR FIELDS

@article{Zhao2011LIMITCF, title={LIMIT CYCLES FOR PLANAR SEMI-QUASI-HOMOGENEOUS POLYNOMIAL VECTOR FIELDS}, author={Yulin Zhao}, journal={Journal of Mathematical Analysis and Applications}, year={2011}, volume={397}, pages={276-284} }

## 9 Citations

### Global Structure of Planar Quadratic Semi-Quasi-Homogeneous Polynomial Systems

- Mathematics
- 2019

This paper study the planar quadratic semi-quasi-homogeneous polynomial systems(short for PQSQHPS). By using the nilpotent singular points theorem, blow-up technique, Poincaré index formula, and…

### Planar Semi-quasi Homogeneous Polynomial Differential Systems with a Given Degree

- MathematicsQualitative Theory of Dynamical Systems
- 2019

This paper study the planar semi-quasi homogeneous polynomial differential systems (PSQHPDS), which can be regarded as a generalization of semi-homogeneous and of quasi-homogeneous systems. By using…

### Planar Semi-quasi Homogeneous Polynomial Differential Systems with a Given Degree

- MathematicsQualitative Theory of Dynamical Systems
- 2019

This paper study the planar semi-quasi homogeneous polynomial differential systems (PSQHPDS), which can be regarded as a generalization of semi-homogeneous and of quasi-homogeneous systems. By using…

### Planar quasi-homogeneous polynomial systems with a given weight degree

- Mathematics
- 2016

In this paper, we investigate a class of quasi-homogeneous polynomial systems with a given weight degree. Firstly, by some analytical skills, several properties about this kind of systems are derived…

### Limit cycles and global dynamic of planar cubic semi-quasi-homogeneous systems

- MathematicsDiscrete & Continuous Dynamical Systems - B
- 2021

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…

### On the Limit Cycles Bifurcating from Piecewise Quasi-Homogeneous Differential Center

- MathematicsInt. J. Bifurc. Chaos
- 2016

A lower bound of the maximum number of limit cycles which bifurcate from the periodic annulus of the center under polynomial perturbation is obtained using the first order Melnikov function derived in Liu & Han, 2010.

### Bifurcation of limit cycles and center problem for p:q homogeneous weight systems

- MathematicsNonlinear Analysis: Real World Applications
- 2019

### Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities

- Mathematics
- 2013

### Center-focus determination and limit cycles bifurcation for $p:q$ homogeneous weight singular point

- Mathematics
- 2016

The quasi-homogeneous (and in general non-homogeneous) polynomial differential systems have been studied from many different points of view. In this paper, Center-focus determination and limit cycles…

## References

SHOWING 1-10 OF 35 REFERENCES

### Cyclicity of a family of vector fields

- Mathematics
- 1995

Abstract We study the cyclicity and the center problem for a special family of planar differential equations. We also relate this cyclicity With the maximum number of limit cycles that bifurcate from…

### Lie Symmetries of Quasihomogeneous Polynomial Planar Vector Fields and Certain Perturbations

- Mathematics
- 2005

In this work we study Lie symmetries of planar quasihomogeneous polynomial vector fields from different points of view, showing its integrability. Additionally, we show that certain perturbations of…

### Structural Stability of Planar Homogeneous Polynomial Vector Fields: Applications to Critical Points and to Infinity

- Mathematics
- 1996

LetHmbe the space of planar homogeneous polynomial vector fields of degreemendowed with the coefficient topology. We characterize the setΩmof the vector fields ofHmthat are structurally stable with…

### Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem

- Mathematics
- 1998

Preface.- 1 Families of Two-dimensional Vector Fields.- 2 Limit Periodic Sets.- 3 The 0-Parameter Case.- 4 Bifurcations of Regular Limit Periodic Sets.- 5 Bifurcations of Elementary Graphics.- 6…

### Limit Cycles Bifurcating from the Period Annulus of Quasi-Homogeneous Centers

- Mathematics
- 2009

We provide upper bounds for the maximum number of limit cycles bifurcating from the period annulus of any homogeneous and quasi-homogeneous center, which can be obtained using the Abelian integral…

### Structural stability of planar semi-homogeneous polynomial vector fields applications to critical points and to infinity

- Mathematics
- 2000

Recently, in [9] we characterized the set of planar
homogeneous
vector fields that are structurally stable and we obtained the exact number
of the topological equivalence classes.
Furthermore, we…

### Topological equivalence of a plane vector field with its principal part defined through Newton Polyhedra

- Mathematics
- 1990

### Qualitative Theory of Planar Differential Systems

- Mathematics
- 2006

This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic…

### Differential Equations Defined by the Sum of two Quasi-Homogeneous Vector Fields

- MathematicsCanadian Journal of Mathematics
- 1997

Abstract In this paper we prove, that under certain hypotheses, the planar differential equation: ˙x = X 1(x, y) + X 2(x, y), ˙y = Y 1(x, y) + Y 2(x, y), where (X i , Y i ), i = 1, 2, are…