منابع مشابه
Stochastic delay Lotka–Volterra model
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 the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but few for their stochastic counterparts. The food chain we analyze consists of one prey and [Formula: see text] predators. The jth predator eats the [Formula:...
متن کاملCoexistence 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-...
متن کاملNon-equilibrium relaxation in a stochastic lattice Lotka-Volterra model.
We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates ...
متن کاملAsymptotic behaviour of the stochastic Lotka–Volterra model
This paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process, namely the Lotka–Volterra model. The stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart. Indeed, the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amo...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2011
ISSN: 1029-242X
DOI: 10.1155/2011/914270