Limit cycles of a class of planar polynomial differential systems

2021 ◽  
Author(s):  
Nassima Debz ◽  
Amel Boulfoul ◽  
Abdelhak Berkane
Keyword(s):  
Limit Cycles ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Planar Polynomial Differential Systems

scholarly journals Upper bounds for the number of limit cycles of some planar polynomial differential systems

2010 ◽  
Vol 27 (1) ◽  
pp. 217-229 ◽  
Author(s):  
Armengol Gasull ◽  
◽  
Hector Giacomini ◽  
Keyword(s):  
Limit Cycles ◽  
Upper Bounds ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Planar Polynomial Differential Systems

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.

Geometric Configurations of Singularities of Planar Polynomial Differential Systems

2021 ◽  
Author(s):  
Joan C. Artés ◽  
Jaume Llibre ◽  
Dana Schlomiuk ◽  
Nicolae Vulpe
Keyword(s):  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Geometric Configurations ◽  
Planar Polynomial Differential Systems

scholarly journals The Cubic Polynomial Differential Systems with two Circles as Algebraic Limit Cycles

2018 ◽  
Vol 18 (1) ◽  
pp. 183-193 ◽  
Author(s):  
Jaume Giné ◽  
Jaume Llibre ◽  
Claudia Valls
Keyword(s):  
Limit Cycles ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Cubic Polynomial ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit

AbstractIn this paper we characterize all cubic polynomial differential systems in the plane having two circles as invariant algebraic limit cycles.

scholarly journals Limit Cycles for a Class of Three-Dimensional Polynomial Differential Systems

2007 ◽  
Vol 13 (4) ◽  
pp. 531-539 ◽  
Author(s):  
Jaume Llibre ◽  
Jiang Yu
Keyword(s):  
Limit Cycles ◽  
Three Dimensional ◽  
Differential Systems ◽  
Polynomial Differential Systems

scholarly journals Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

2014 ◽  
Vol 13 (1) ◽  
pp. 129-148 ◽  
Author(s):  
Jaume Llibre ◽  
Bruno D. Lopes ◽  
Jaime R. De Moraes
Keyword(s):  
Limit Cycles ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Cubic Polynomial
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