caa a22 4500 606233385 CHVBK 20210128101231.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10883-015-9282-7 doi (NATIONALLICENCE)springer-10.1007/s10883-015-9282-7 Żoła̧dek Henryk Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland aut Melnikov Functions in Quadratic Perturbations of Generalized Lotka-Volterra Systems [Elektronische Daten] [Henryk Żoła̧dek] 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 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. Springer Science+Business Media New York, 2015 Quadratic plane vector fields nationallicence Lotka-Volterra systems nationallicence Limit cycles nationallicence Melnikov functions nationallicence Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/4(2015-10-01), 573-603 1079-2724 21:4<573 2015 21 10883 https://doi.org/10.1007/s10883-015-9282-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10883-015-9282-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Żoła̧dek Henryk Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/4(2015-10-01), 573-603 1079-2724 21:4<573 2015 21 10883