Extinction in the Lotka-Volterra model
نویسندگان
چکیده
منابع مشابه
Extinction in Lotka-Volterra model
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...
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 کاملExtinction in Competitive Lotka-volterra Systems
It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to arbitrary finite dimension. That is, for the «-species autonomous competitive Lotka-Volte...
متن کاملExtinction in Nonautonomous Competitive Lotka-volterra Systems
It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to nonautonomous systems of arbitrary finite dimension. That is, for the n species nonautono...
متن کاملExtinction of Species in Nonautonomous Lotka-volterra Systems
A nonautonomous nth order Lotka-Volterra system of differential equations is considered. It is shown that if the coefficients satisfy certain inequalities, then any solution with positive components at some point will have all of its last n − 1 components tend to zero, while the first one will stabilize at a certain solution of a logistic equation.
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2009
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.80.021129