Home > Articles > Published articles > On the period function in a class of generalized Lotka-Volterra systems |
Date: | 2010 |
Abstract: | In this note, motivated by the recent results of Wang et al. [Wang et al. , Local bifurcations of critical periods in a generalized 2D LV system, Appl. Math. Comput. 214 (2009) 17-25], we study the behaviour of the period function of the center at the point (1,1) of the planar differential system {u' = up(1−vq),v'= μvq(up−1), where p, q, μ ∈ R with pq > 0 and μ > 0. Our aim is twofold. Firstly, we determine regions in the parameter space for which the corresponding system has a center with a monotonic period function. Secondly, by taking advantage of the results of Wang et al. , we show some properties of the bifurcation diagram of the period function and we make some comments for further research. The differential system under consideration is a generalization proposed by Farkas and Noszticzius of the Lotka-Volterra model. |
Grants: | Ministerio de Ciencia y Tecnología MTM-2005-06098-C02-01 Agència de Gestió d'Ajuts Universitaris i de Recerca 2005/SGR-00550 |
Rights: | Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Lotka-Volterra model ; Center ; Period function ; Critical period |
Published in: | Applied Mathematics and Computation, Vol. 216, Issue 7 (June 2010) , p. 1956-1964, ISSN 1873-5649 |
Postprint 12 p, 630.6 KB |