Bounding the quality of stochastic oscillations in population models
Centro Atómico Bariloche and CONICET, 8400 S.C. de Bariloche, Argentina
2 Instituto Balseiro, 8400 S.C. de Bariloche, Argentina
Revised: 8 October 2007
Published online: 16 January 2008
We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. Although usually defined a priori, the deterministic version of these models can be obtained as the infinite volume limit of many stochastic models (which are necessarily defined by more parameters than the deterministic one). It is known that damped oscillations in a deterministic model usually correspond to oscillatory-like fluctuations in their deterministic counterparts. The quality of these “oscillations" depends on details of each stochastic model. We show, however, that the parameters of the deterministic system are generally enough to obtain very good bounds for the quality of “oscillations" in any of its stochastic counterparts. These bounds are shown to depend on only one dimensionless parameter.
PACS: 87.23.Cc – Population dynamics and ecological pattern formation / 02.50.Ey – Stochastic processes / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008