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Steady states of lattice population models with immigration

Chernousova, E; Feng, Y; Hryniv, O; Molchanov, S; Whitmeyer, J

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Authors

E Chernousova

Y Feng

S Molchanov

J Whitmeyer



Abstract

In a lattice population model where individuals evolve as subcritical branching random walks subject to external immigration, the cumulants are estimated and the existence of the steady state is proved. The resulting dynamics are Lyapunov stable in that their qualitative behavior does not change under suitable perturbations of the main parameters of the model. An explicit formula of the limit distribution is derived in the solvable case of no birth. Monte Carlo simulation shows the limit distribution in the solvable case.

Citation

Chernousova, E., Feng, Y., Hryniv, O., Molchanov, S., & Whitmeyer, J. (2021). Steady states of lattice population models with immigration. Mathematical Population Studies, 28(2), 63-80. https://doi.org/10.1080/08898480.2020.1767411

Journal Article Type Article
Online Publication Date Jun 12, 2020
Publication Date 2021
Deposit Date Aug 8, 2018
Publicly Available Date Dec 12, 2021
Journal Mathematical Population Studies
Print ISSN 0889-8480
Electronic ISSN 1547-724X
Publisher Taylor and Francis Group
Peer Reviewed Peer Reviewed
Volume 28
Issue 2
Pages 63-80
DOI https://doi.org/10.1080/08898480.2020.1767411
Public URL https://durham-repository.worktribe.com/output/1318261

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