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Extinction threshold in the spatial stochastic logistic model: space homogeneous case / Dmitri Finkelshtein

Applicable Analysis, Pages: 1 - 28

Swansea University Author: Dmitri, Finkelshtein

Abstract

We consider the extinction regime in the spatial stochastic logistic model in R^d (a.k.a. Bolker–Pacala–Dieckmann–Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space homogeneous case (i.e. when the density is non-spatial and the covariance is...

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Published in: Applicable Analysis
ISSN: 0003-6811 1563-504X
Published: Informa UK Limited
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa55219
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Abstract: We consider the extinction regime in the spatial stochastic logistic model in R^d (a.k.a. Bolker–Pacala–Dieckmann–Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space homogeneous case (i.e. when the density is non-spatial and the covariance is translation invariant), we show that the perturbation converges as time tends to infinity; that yields the first-order approximation for the stationary density. Next, we study the critical mortality – the smallest constant death rate which ensures the extinction of the population – as a function of the mean-field scaling parameter ε>0. We find the leading term of the asymptotic expansion (as ε→0) of the critical mortality which is apparently different for the cases d≥3, d = 2, and d = 1.
College: College of Science
Start Page: 1
End Page: 28