Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
نویسندگان
چکیده
منابع مشابه
Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model.
Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see, e.g., B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature 418, 171 (2002)] and B. Kirkup and M. A. Riley [Nature 428, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-...
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Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey competition. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the syste...
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We reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay Lotka–Volterra model but will also make the solutions to be stochastically ultimately bounded. To reveal these interesting facts, we stochastically perturb the delay Lotka–Volterra model ẋ(t) = diag(x1(t), . . . , xn(t))[b + Ax(t − τ)] into the Itô form dx(t)= dia...
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We study a cyclic Lotka-Volterra model of N interacting species populating a d-dimensional lattice. In the realm of a Kirkwood approximation, a critical number of species Nc(d) above which the system fixates is determined analytically. We find Nc = 5, 14, 23 in dimensions d = 1, 2, 3, in remarkably good agreement with simulation results in two dimensions. A cyclic variant of the Lotka-Volterra ...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2006
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.74.051907