The cyclicity and period function of a class of quadratic reversible Lotka-Volterra system of genus one
type: Item
instance of: scholarly article
title: The cyclicity and period function of a class of quadratic reversible Lotka-Volterra system of genus one
zbMATH Open document ID: 1219.34044
author: Yi Shao
author: Yulin Zhao
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-03-08T00:00:00Z
review text: The authors consider a quadratic reversible Lotka-Volterra system of genus one that possesses a first integral with a center. As has been done by different authors, they investigate the cyclicity of the corresponding period annulus, i.e., the maximal number of limit cycles that emerge under arbitrary quadratic perturbations of the system. It is proved that the cyclicity is two, and that the period function of the center is strictly monotone. The proof utilizes standard tools in the field, such as the Picard-Fuchs equations for Abelian integrals, the Riccati equation for ratios of Abelian integrals, and their derivatives, rsp.
reviewed by: Josef Hainzl
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C08
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 5862732
zbMATH Keywords: quadratic center
zbMATH Keywords: limit cycle
zbMATH Keywords: Abelian integral
zbMATH Keywords: period function
zbMATH Keywords: cyclicity
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.11.048
OpenAlex ID: W2000823952
cites work: Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops
cites work: Quadratic centers defining elliptic surfaces
cites work: Perturbations of quadratic centers of genus one
cites work: Cyclicity of period annuli and principalization of Bautin ideals
cites work: Two-dimensional Fuchsian systems and the Chebyshev property.
cites work: A Chebyshev criterion for Abelian integrals
cites work: Q5330830
cites work: A remark on the period of the periodic solution in the Lotka-Volterra system
cites work: Perturbations of quadratic centers
cites work: Bifurcations of limit cycles from quadratic non-Hamiltonian systems with two centres and two unbounded heteroclinic loops
cites work: Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes
cites work: Quadratic perturbations of a quadratic reversible Lotka-Volterra system
cites work: The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system
cites work: The bifurcation set of the period function of the dehomogenized Loud's centers is bounded
cites work: The period function of reversible quadratic centers
cites work: The periods of the Volterra-Lotka system.
cites work: The period in the Lotka-Volterra system is monotonic
cites work: Bifurcation of a class of planar non-Hamiltonian integrable systems with one center and one homoclinic loop
cites work: The monotonicity of period function for the codimension four quadratic system \(Q_4\).
cites work: On the monotonicity of the period function of a quadratic system
cites work: The cyclicity of the period annulus of the quadratic Hamiltonian systems with non-Morsean point
cites work: Quadratic systems with center and their perturbations
DOI: 10.1016/J.JMAA.2010.11.048
description: scientific article; zbMATH DE number 5862732