On a stochastic Ricker competition model

Göran Högnäs

On a stochastic Ricker competition model

Göran Högnäs

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Sammanfattning

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.

Originalspråk	Odefinierat/okänt
Titel på värdpublikation	Difference Equations, Discrete Dynamical Systems and Applications
Redaktörer	Lluís Alsedà i Soler, Jim M. Cushing, Saber Elaydi, Alberto Adrego Pinto
Förlag	Springer
Sidor	135–144
ISBN (elektroniskt)	978-3-662-52927-0
ISBN (tryckt)	978-3-662-52926-3
Status	Publicerad - 2016
MoE-publikationstyp	A4 Artikel i en konferenspublikation
Evenemang	18th International Conference on Difference Equations and Applications - 18th International Conference on Difference Equations and Applications Varaktighet: 23 juli 2012 → 27 juli 2012

Konferens

Konferens	18th International Conference on Difference Equations and Applications
Period	23/07/12 → 27/07/12

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title = "On a stochastic Ricker competition model",

abstract = "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.",

author = "G{\"o}ran H{\"o}gn{\"a}s",

year = "2016",

language = "Odefinierat/ok{\"a}nt",

isbn = "978-3-662-52926-3",

pages = "135–144",

editor = "\{Alsed{\`a} i Soler\}, Llu{\'i}s and Cushing, \{Jim M.\} and Saber Elaydi and \{Adrego Pinto\}, Alberto",

booktitle = "Difference Equations, Discrete Dynamical Systems and Applications",

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note = "18th International Conference on Difference Equations and Applications ; Conference date: 23-07-2012 Through 27-07-2012",

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T1 - On a stochastic Ricker competition model

AU - Högnäs, Göran

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

M3 - Publicerad konferensartikel

SN - 978-3-662-52926-3

SP - 135

EP - 144

BT - Difference Equations, Discrete Dynamical Systems and Applications

A2 - Alsedà i Soler, Lluís

A2 - Cushing, Jim M.

A2 - Elaydi, Saber

A2 - Adrego Pinto, Alberto

PB - Springer

T2 - 18th International Conference on Difference Equations and Applications

Y2 - 23 July 2012 through 27 July 2012

ER -