scholarly journals Non-existence and uniqueness of limit cycles for planar polynomial differential systems with homogeneous nonlinearities

2018 ◽  
Vol 265 (9) ◽  
pp. 3888-3913 ◽  
Author(s):  
Jianfeng Huang ◽  
Haihua Liang ◽  
Jaume Llibre
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Uniqueness Of Limit Cycles ◽  
Planar Polynomial Differential Systems

scholarly journals The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems

2017 ◽  
Vol 149 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Jaume Llibre ◽  
Xiang Zhang
Keyword(s):  
Differential System ◽  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Quadratic Polynomial ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Polynomial Differential System ◽  
Uniqueness Of Limit Cycles

AbstractWe provide sufficient conditions for the non-existence, existence and uniqueness of limit cycles surrounding a focus of a quadratic polynomial differential system in the plane.

scholarly journals Existence and Uniqueness of Limit Cycles in a Class of Planar Differential Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Khalil I. T. Al-Dosary
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Differential Systems ◽  
Uniqueness Of Limit Cycles

This paper is an extension to the recent results presented by M. Sabatini about the existence and uniqueness of limit cycles of a certain class of planar differential systems in order to include other new classes. A concrete example exhibiting the applicability of the result is introduced.

Limit Cycles for a Class of Zp-Equivariant Differential Systems

2020 ◽  
Vol 30 (08) ◽  
pp. 2050115
Author(s):  
Jing Gao ◽  
Yulin Zhao
Keyword(s):  
Differential System ◽  
Limit Cycles ◽  
Melnikov Function ◽  
Differential Systems ◽  
First Order ◽  
Polynomial Differential Systems ◽  
Number Of Zeros ◽  
Planar Polynomial Differential Systems

In this paper, we study a class of [Formula: see text]-equivariant planar polynomial differential systems [Formula: see text]. It is shown that for any [Formula: see text] there is a differential system of the above type having at least [Formula: see text] limit cycles. This is proved by estimating the number of zeros of the first-order Melnikov function.

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