The cyclicity and period function of a class of quadratic reversible Lotka–Volterra system of genus one

Shao, Yi; Zhao, Yulin

doi:10.1016/j.jmaa.2010.11.048

Cited by 15 publications

(2 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The cyclicity of the center of (rlv3) was verified in [3], by using the criterion which provides sufficient conditions in order that a collection of Abelian integrals have the Chebyshev property. The reference [5] and [10] respectively study the case b = 0 and the case b = 3/5 (i.e the case (rlv4)), and all the above verify the conjecture of [2]. It is worth noting that (rlv1)-(rlv4) are systems with single center, while (rlv5) and (rlv6) have two different types of centers with two unbounded period annuli.…”

Section: Introductionsupporting

confidence: 55%

The cyclicity of period annuli of a quadratic reversible Lotka-Volterra system with two centers

Wu¹

2015

nade

View full text Add to dashboard Cite

This paper is concerned with the bifurcations of limit cycles in a quadratic reversible Lotka-Volterra system with two centers under quadratic perturbations. By studying the number of zeros of Abelian integral based on the geometric properties of some planar curves, we obtain the cyclicity of each periodic annulus of the system under quadratic perturbations is two, and the cyclicity of two period annuli is three. In addition, we present the configurations of limit cycles of the perturbed system.

show abstract

Section: Introductionsupporting

confidence: 55%

The cyclicity of period annuli of a quadratic reversible Lotka-Volterra system with two centers

Wu¹

2015

nade

View full text Add to dashboard Cite

show abstract

“…However, in recent years, there were some works on limit cycle bifurcations by perturbing non-Hamilton integrable systems (see [7,13,[15][16][17] for example). As we know, the main tool for studying the bifurcation problem of limit cycles is to use the first order Melnikov function.…”

Section: Introductionmentioning

confidence: 99%

Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle

Wang

Han

2014

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

In this paper, we deal with the problem of limit cycle bifurcation near a 2-polycycle or 3-polycycle for a class of integrable systems by using the first order Melnikov function. We first get the formal expansion of the Melnikov function corresponding to the heteroclinic loop and then give some computational formulas for the first coefficients of the expansion. Based on the coefficients, we obtain a lower bound for the maximal number of limit cycles near the polycycle. As an application of our main results, we consider quadratic integrable polynomial systems, obtaining at least two limit cycles.

show abstract

Limit cycles bifurcating from a quadratic reversible Lotka-Volterra system with a center and three saddles

Liang

2014

Chin. Ann. Math. Ser. B

View full text Add to dashboard Cite

The cyclicity and period function of a class of quadratic reversible Lotka–Volterra system of genus one

Cited by 15 publications

References 21 publications

The cyclicity of period annuli of a quadratic reversible Lotka-Volterra system with two centers

The cyclicity of period annuli of a quadratic reversible Lotka-Volterra system with two centers

Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle

Limit cycles bifurcating from a quadratic reversible Lotka-Volterra system with a center and three saddles

Contact Info

Product

Resources

About