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.

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.

On the nonexistence, existence and uniqueness of limit cycles

Nonlinearity ◽  
1996 ◽  
Vol 9 (2) ◽  
pp. 501-516 ◽  
Author(s):  
H Giacomini ◽  
J Llibre ◽  
M Viano
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Uniqueness Of Limit Cycles

scholarly journals On the existence and uniqueness of limit cycles in planar refracted systems

2019 ◽  
Vol 51 (4) ◽  
pp. 605
Author(s):  
Li Shimin ◽  
Chen Ting ◽  
Liu Yuji ◽  
Li Xiaoli
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Uniqueness Of Limit Cycles

scholarly journals Limit cycles in a Kolmogorov-type model

1990 ◽  
Vol 13 (3) ◽  
pp. 555-566 ◽  
Author(s):  
Xun-Cheng Huang
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Equilibrium Points ◽  
Type Model ◽  
Kolmogorov Type ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stability Of Equilibrium ◽  
Uniqueness Of Limit Cycles ◽  
The Stability

In this paper, a Kolmogorov-type model, which includes the Gause-type model (Kuang and Freedman, 1988), the general predator-prey model (Huang 1988, Huang and Merrill 1989), and many other specialized models, is studied. The stability of equilibrium points, the existence and uniqueness of limit cycles in the model are proved.

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