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

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.