Steady states of lattice population models with immigration

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

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