Bounding the quality of stochastic oscillations in population models |
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Authors: | S Risau-Gusman G Abramson |
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Institution: | (1) Centro Atómico Bariloche and CONICET, 8400 S.C. de Bariloche, Argentina;(2) Instituto Balseiro, 8400 S.C. de Bariloche, Argentina |
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Abstract: | 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. |
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Keywords: | 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 |
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