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Extinction threshold in the spatial stochastic logistic model: space homogeneous case
Dmitri Finkelshtein 
Applicable Analysis, Volume: 101, Issue: 7, Pages: 2726 - 2753
Swansea University Author:
Dmitri Finkelshtein
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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...
| Published in: | Applicable Analysis |
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| ISSN: | 0003-6811 1563-504X |
| Published: |
Informa UK Limited
2022
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| Online Access: |
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| 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. |
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| Keywords: |
Extinction threshold, spatial logistic model, mean-field equation, population density, perturbation, correlation function, asymptotic behaviour |
| College: |
Faculty of Science and Engineering |
| Issue: |
7 |
| Start Page: |
2726 |
| End Page: |
2753 |