Probabilities of extinction, weak extinction permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems
نویسندگان
چکیده
منابع مشابه
Extinction 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 کاملCompetitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction.
We are interested in the long time behavior of a two-type density-dependent biological population conditioned on non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a stochastic Lotka-Volterra system, obtained as limit of renormalized interacting birth and death processes. The weak cooperation assumption allows the system not...
متن کاملCompetitive or Weak Cooperative Stochastic Lotka-volterra Systems Conditioned to Non-extinction
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a stochastic LotkaVolterra system, obtained as limit of renormalized interacting birth and death processes. The weak cooperation assumption allows the system not ...
متن کاملExtinction 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...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2004
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(04)90031-4