文摘
We present a detailed analysis of Melnikov functions which arise in quadratic perturbations of generalized Lotka–Volterra vector fields with the first integral x α y β (1 ?x ?y). That analysis was sketched in ?o?a?dek (J Differ Equ 109:223-73, 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. Keywords Quadratic plane vector fields Lotka–Volterra systems Limit cycles Melnikov functions