On a stochastic Ricker competition model

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Internal Authors/Editors

Publication Details

List of Authors: Göran Högnäs
Editors: Lluís Alsedà i Soler, Jim M. Cushing, Saber Elaydi, Alberto Adrego Pinto
Place: Berlin, Heidelberg
Publication year: 2016
Publisher: Springer
Book title: Difference Equations, Discrete Dynamical Systems and Applications
Title of series: Springer Proceedings in Mathematics & Statistics
Volume number: 180
Start page: 135
End page: 144
ISBN: 978-3-662-52926-3
eISBN: 978-3-662-52927-0
ISSN: 2194-1009


We model the evolution of two competing populations by a two-dimensional size-dependent branching process of Ricker type. For a small force of inhibition by the present population (modeling, e.g., scarcity of food) the process typically follows the corresponding deterministic Ricker competition model closely, for a very long time. Under some conditions, notably a mutual invasibility condition, the deterministic model has a coexistence fixed point in the open first quadrant. The asymptotic behaviour is studied through the quasi-stationary distribution of the process. We initiate a study of those distributions as the inhibitive force approach 0.

Last updated on 2019-12-11 at 04:47