Bifurcation of limit cycles for quadratic reversible Lotka-Volterra systems with non-genus one

WU Sha; WU Kuilin

doi:10.13471/j.cnki.acta.snus.2022A083

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Bifurcation of limit cycles for quadratic reversible Lotka-Volterra systems with non-genus one

Research articles | 更新时间：2023-12-08

- Bifurcation of limit cycles for quadratic reversible Lotka-Volterra systems with non-genus one
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 62, Issue 6, Pages: 127-134(2023)
- 作者机构：
  
  贵州大学数学与统计学院，贵州贵阳 550025
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2022A083
  CLC： O175.21
- Published：25 November 2023，
  
  Published Online：27 July 2023，
  
  Received：27 September 2022，
  
  Accepted：26 February 2023
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吴莎,吴奎霖.亏格不为1的二次可逆LV系统的极限环分支[J].中山大学学报(自然科学版),2023,62(06):127-134.

WU Sha,WU Kuilin.Bifurcation of limit cycles for quadratic reversible Lotka-Volterra systems with non-genus one[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(06):127-134.
吴莎,吴奎霖.亏格不为1的二次可逆LV系统的极限环分支[J].中山大学学报(自然科学版),2023,62(06):127-134. DOI： 10.13471/j.cnki.acta.snus.2022A083.

WU Sha,WU Kuilin.Bifurcation of limit cycles for quadratic reversible Lotka-Volterra systems with non-genus one[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(06):127-134. DOI： 10.13471/j.cnki.acta.snus.2022A083.

摘要

主要研究两个亏格不为1的二次可逆Lotka-Volterra系统的周期环域在小扰动下产生极限环的个数问题. 应用完全切比雪夫系统的性质来判定该系统的二阶Melnikov函数的零点个数，从而证明了在二次扰动下，这两个系统的周期环域能分支出两个极限环.

Abstract

The number of limit cycles bifurcated from the periodic annulus of two quadratic reversible Lotka-Volterra systems with non-genus 1 under small bifurcations is studied. Using the properties of complete Chebyshev systems to estimate the number of zeros of second-order Melnikov function， it is proven that the number of limit cycles bifurcated from the periodic annulus of the two quadratic reversible Lotka-Volterra systems are both 2 under quadratic perturbations.

关键词

可逆LV系统Abel积分极限环亏格1

Keywords

reversible Lotka-Volterra systemAbelian integrallimit cyclesgenus one

references

BORWEIN P B， ERDÉLYI T， 1995. Polynomials and polynomial inequalities［M］. New York： Springer Verlag.

GAUTIER S， GAVRILOV L， ILIEV I D， 2009. Perturbations of quadratic centers of genus one［J］. Discrete Contin Dyn Syst， 25（2）： 511-535.

GAVRILOV L， ILIEV I D， 2000. Second-order analysis in polynomially perturbed reversible quadratic Hamiltonian systems［J］. Ergod Th Dynam Sys， 20（6）： 1671-1686.

GAVRILOV L， ILIEV I D， 2009. Quadratic perturbations of quadratic codimension-four centers［J］. J Math Anal Appl， 357（1）： 69-76.

GRAU M， MAÑOSAS F， VILLADELPRAT J， 2011. A Chebyshev criterion for abelian integrals［J］. Trans Amer Math Soc， 363（1）： 109-129.

HOROZOV E， ILIEV I D， 1994. On the number of limit cycles in perturbations of quadratic Hamiltonian systems［J］. Proc Lond Math Soc， 69（1）： 198-224.

ILIEV I D， 1996. The cyclicity of the period annulus of the quadratic Hamiltonian triangle［J］. J Differ Equ， 128（1）： 309-326.

ILIEV I D， 1997. Inhomogeneous Fuchs equations and the limit cycles in a class of near-integrable quadratic systems［J］. Proc Roy Soc Edinburgh Sect A， 127（6）： 1207-1217.

ILIEV I D， 1998. Perturbations of quadratic centers［J］. Bull Sci Math， 122（2）： 107-161.

LI C， LLIBRE J， 2009. The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system［J］. Nonlinearity， 22（12）： 2971-2979.

LI C Z， ZHANG Z， 2002. Remarks on 16th weak Hilbert problem for <math id="M254"><mi>n</mi><mo>=</mo><mn mathvariant="normal">2</mn></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51094556&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51094554&type=7.111999992.28600001［J］. Nonlinearity， 15（6）： 1975-1992.

LIU C J， 2012. The cyclicity of period annuli of a class of quadratic reversible systems with two centers［J］. J Differ Equ， 252（10）： 5260-5273.

PENG L P， FENG Z S， LIU C J， 2014. Quadratic perturbations of a quadratic reversible Lotka-Volterra systems with two centers［J］. Discrete Contin Dyn Syst， 34（11）： 4807-4826.

SHAO Y， CHUNXIANG A， 2013. Quadratic perturbations of a class of quadratic reversible Lotka-Volterra systems［J］. Int J Bifur Chaos， 23（8）： 1350137.

SHAO Y， ZHAO Y L， 2011. The cyclicity and period function of a class of quadratic reversible Lotka-Volterra system of genus one［J］. J Math Anal Appl， 377（2）： 817-827.

WU K L， LIANG H H， 2014. Limit cycles bifurcating from a quadratic reversible Lotka-Volterra system with a center and three saddles［J］. Chin Ann Math Ser B， 35： 25-32.

ZHAO Y L， 2011. On the number of limit cycles in quadratic perturbations of quadratic codimension-four centres［J］. Nonlinearity， 24（9）： 2505-2522.

ZOLADEK H， 1994. Quadratic systems with center and their perturbations［J］. J Differ Equ， 109（2）： 223-273.

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