Nonexistence of limit cycles for a class of structurally stable quadratic vector fields

2007 ◽  
Vol 17 (2) ◽  
pp. 259-270 ◽  
Author(s):  
J. C. Artés ◽  
◽  
Jaume Llibre ◽  
J. C. Medrado ◽  
◽  
...  
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Quadratic Vector Fields ◽  
Structurally Stable

Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry

2018 ◽  
Vol 28 (11) ◽  
pp. 1850139 ◽  
Author(s):  
Laigang Guo ◽  
Pei Yu ◽  
Yufu Chen
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Center Manifold ◽  
Three Dimensional ◽  
Center Manifold Theory ◽  
Normal Form Theory ◽  
Quadratic Vector Fields ◽  
Fine Focus ◽  
Form Theory ◽  
Manifold Theory

This paper is concerned with the number of limit cycles bifurcating in three-dimensional quadratic vector fields with [Formula: see text] symmetry. The system under consideration has three fine focus points which are symmetric about the [Formula: see text]-axis. Center manifold theory and normal form theory are applied to prove the existence of 12 limit cycles with [Formula: see text]–[Formula: see text]–[Formula: see text] distribution in the neighborhood of three singular points. This is a new lower bound on the number of limit cycles in three-dimensional quadratic systems.

scholarly journals Uniqueness of limit cycles for quadratic vector fields

2019 ◽  
Vol 39 (1) ◽  
pp. 483-502
Author(s):  
José Luis Bravo ◽  
◽  
Manuel Fernández ◽  
Ignacio Ojeda ◽  
Fernando Sánchez
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Quadratic Vector Fields ◽  
Uniqueness Of Limit Cycles

Structurally stable quadratic vector fields

1998 ◽  
Vol 134 (639) ◽  
pp. 0-0 ◽  
Author(s):  
Joan C. Artés ◽  
Robert E. Kooij ◽  
Jaume Llibre
Keyword(s):  
Vector Fields ◽  
Quadratic Vector Fields ◽  
Structurally Stable

Cyclicity of a Family of Generic Reversible Quadratic Systems with One Center

2019 ◽  
Vol 29 (03) ◽  
pp. 1950035 ◽  
Author(s):  
Jihua Wang ◽  
Yanfei Dai
Keyword(s):  
Limit Cycles ◽  
Upper Bound ◽  
Vector Fields ◽  
Parameter Family ◽  
Reversible Systems ◽  
Abelian Integrals ◽  
Quadratic Systems ◽  
Quadratic Vector Fields ◽  
Period Annulus ◽  
Straight Line

This paper is concerned with the quadratic perturbations from one parameter family of generic reversible quadratic vector fields having a simple center and an invariant straight line. It is shown that the system can generate at least two limit cycles. As the parameter is rational, we propose a procedure for finding the upper bound to cyclicity of period annulus based on the Chebyshev criterion for Abelian integrals together with one rationalizing transformation. To illustrate our approach, we determine the cyclicity of three representative reversible systems. Our results may be viewed as a contribution to proving the conjecture on cyclicity proposed by Iliev [1998].

Sign in / Sign up

Export Citation Format

Share Document