Resolution of the Poincaré problem and nonexistence of algebraic limit cycles in family (I) of Chinese classification☆

2005 ◽  
Vol 24 (2) ◽  
pp. 491-499 ◽  
Author(s):  
Javier Chavarriga ◽  
Isaac A. García ◽  
Jordi Sorolla
Keyword(s):  
Limit Cycles ◽  
Poincaré Problem ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit

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 On the 16th Hilbert problem for algebraic limit cycles

2010 ◽  
Vol 248 (6) ◽  
pp. 1401-1409 ◽  
Author(s):  
Jaume Llibre ◽  
Rafael Ramírez ◽  
Natalia Sadovskaia
Keyword(s):  
Limit Cycles ◽  
Hilbert Problem ◽  
16Th Hilbert Problem ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit

scholarly journals Non-nested configuration of algebraic limit cycles in quadratic systems

2006 ◽  
Vol 225 (2) ◽  
pp. 513-527 ◽  
Author(s):  
J. Chavarriga ◽  
I.A. García ◽  
J. Sorolla
Keyword(s):  
Limit Cycles ◽  
Quadratic Systems ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit

scholarly journals Non-algebraic limit cycles in Holling type III zooplankton-phytoplankton models

Cubo (Temuco) ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 343-355
Author(s):  
Homero G. Díaz-Marín ◽  
Osvaldo Osuna
Keyword(s):  
Limit Cycles ◽  
Type Iii ◽  
Algebraic Limit Cycles ◽  
Algebraic Limit
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