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

Dmitri Finkelshtein Orcid Logo

Applicable Analysis, Volume: 101, Issue: 7, Pages: 2726 - 2753

Swansea University Author: Dmitri Finkelshtein Orcid Logo

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DOI (Published version): 10.1080/00036811.2020.1820996

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 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa55219
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spelling 2022-07-22T10:50:40.7451084 v2 55219 2020-09-19 Extinction threshold in the spatial stochastic logistic model: space homogeneous case 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2020-09-19 SMA 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. Journal Article Applicable Analysis 101 7 2726 2753 Informa UK Limited 0003-6811 1563-504X Extinction threshold, spatial logistic model, mean-field equation, population density, perturbation, correlation function, asymptotic behaviour 3 5 2022 2022-05-03 10.1080/00036811.2020.1820996 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2022-07-22T10:50:40.7451084 2020-09-19T00:11:38.9893214 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1 55219__18209__277fba7abed4417080e820400a36d2b5.pdf F-Extinction.pdf 2020-09-19T00:49:37.0871179 Output 408980 application/pdf Accepted Manuscript true 2021-09-16T00:00:00.0000000 true eng
title Extinction threshold in the spatial stochastic logistic model: space homogeneous case
spellingShingle Extinction threshold in the spatial stochastic logistic model: space homogeneous case
Dmitri Finkelshtein
title_short Extinction threshold in the spatial stochastic logistic model: space homogeneous case
title_full Extinction threshold in the spatial stochastic logistic model: space homogeneous case
title_fullStr Extinction threshold in the spatial stochastic logistic model: space homogeneous case
title_full_unstemmed Extinction threshold in the spatial stochastic logistic model: space homogeneous case
title_sort Extinction threshold in the spatial stochastic logistic model: space homogeneous case
author_id_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf
author_id_fullname_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf_***_Dmitri Finkelshtein
author Dmitri Finkelshtein
author2 Dmitri Finkelshtein
format Journal article
container_title Applicable Analysis
container_volume 101
container_issue 7
container_start_page 2726
publishDate 2022
institution Swansea University
issn 0003-6811
1563-504X
doi_str_mv 10.1080/00036811.2020.1820996
publisher Informa UK Limited
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2022-05-03T04:09:17Z
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score 10.998002

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