亏格不为1的二次可逆LV系统的极限环分支  

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

作　　者：吴莎 吴奎霖 WU Sha;WU Kuilin(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵州贵阳550025

出　　处：《中山大学学报（自然科学版）（中英文）》2023年第6期127-134,共8页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11661017);贵州省科学技术基金(黔科合基础[2020]1Y405)。

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.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 

分 类 号：O175.21[理学—数学]