Melnikov Functions in Quadratic Perturbations of Generalized Lotka–Volterra Systems
Melnikov Functions in Quadratic Perturbations of Generalized Lotka–Volterra Systems
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DOI：
10.1007/s10883-015-9282-7
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发表时间：
2015-10
影响因子：
0.9
通讯作者：
H. Zoladek
中科院分区：
文献类型：
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作者：
H. Zoladek
本文详细分析了第一积分为x αyβ（1 −x−y）的广义Lotka-Volterra向量场的二次扰动中的Melnikov函数.这一分析在《Differer Equ》（J Differ Equ 109：223-273，1994）中作了概述。特别地，我们证明了一般情况下极限环的最大数量等于2，而在汉密尔顿三角形的情况下，这个数量是3。
We present a detailed analysis of Melnikov functions which arise in quadratic perturbations of generalized Lotka–Volterra vector fields with the first integralxαyβ(1 −x−y). That analysis was sketched in Żoła̧dek (J Differ Equ 109:223–273, 1994). In particular, we prove that the maximal number of limit cycles in the generic case equals 2 and in the Hamiltonian triangle case, this number is 3.