Stochastic prey-predator system with foraging arena scheme

Yongmei Cai; Xuerong Mao

doi:10.1016/j.apm.2018.07.034

Stochastic prey-predator system with foraging arena scheme

Yongmei Cai, Xuerong Mao

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

24 Downloads (Pure)

Abstract

In this paper we extend the foraging arena model describing the dynamics of prey-predator abundance from a deterministic framework to a stochastic one. This is achieved by introducing the environmental noises into the growth rate of prey as well as the death rate of predator populations. We then prove that this stochastic differential equation (SDE) has a unique global positive solution. The long-time behaviours of the system are then developed. Furthermore the existence of a stationary distribution is pointed out under certain parametric restrictions. All the results are illustrated by the computer simulations.

Original language	English
Pages (from-to)	357-371
Number of pages	15
Journal	Applied Mathematical Modelling
Volume	64
Early online date	2 Aug 2018
DOIs	https://doi.org/10.1016/j.apm.2018.07.034
Publication status	Published - 31 Dec 2018

Keywords

stochastic prey-predator model
Brownian motion
extinction
ultimate boundedness
stationary distribution

Access to Document

10.1016/j.apm.2018.07.034

Cai-Mao-AMM-2018-Stochastic-prey-predator-system-with-foragingAccepted author manuscript, 702 KBLicence: CC BY-NC-ND 4.0

Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)
Mao, X. (Principal Investigator)
Royal Society
16/03/17 → 15/06/20
Project: Research Fellowship
Long-time dynamics of numerical solutions of stochastic differential equations
Mao, X. (Principal Investigator)
Royal Society
1/10/16 → 30/09/21
Project: Research
Numerical Analysis of Stochastic Differential Equations: New Challenges
Mao, X. (Principal Investigator)
Leverhulme Trust
1/10/15 → 30/09/17
Project: Research Fellowship

Cite this

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title = "Stochastic prey-predator system with foraging arena scheme",

abstract = "In this paper we extend the foraging arena model describing the dynamics of prey-predator abundance from a deterministic framework to a stochastic one. This is achieved by introducing the environmental noises into the growth rate of prey as well as the death rate of predator populations. We then prove that this stochastic differential equation (SDE) has a unique global positive solution. The long-time behaviours of the system are then developed. Furthermore the existence of a stationary distribution is pointed out under certain parametric restrictions. All the results are illustrated by the computer simulations.",

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author = "Yongmei Cai and Xuerong Mao",

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AU - Cai, Yongmei

AU - Mao, Xuerong

PY - 2018/12/31

Y1 - 2018/12/31

N2 - In this paper we extend the foraging arena model describing the dynamics of prey-predator abundance from a deterministic framework to a stochastic one. This is achieved by introducing the environmental noises into the growth rate of prey as well as the death rate of predator populations. We then prove that this stochastic differential equation (SDE) has a unique global positive solution. The long-time behaviours of the system are then developed. Furthermore the existence of a stationary distribution is pointed out under certain parametric restrictions. All the results are illustrated by the computer simulations.

AB - In this paper we extend the foraging arena model describing the dynamics of prey-predator abundance from a deterministic framework to a stochastic one. This is achieved by introducing the environmental noises into the growth rate of prey as well as the death rate of predator populations. We then prove that this stochastic differential equation (SDE) has a unique global positive solution. The long-time behaviours of the system are then developed. Furthermore the existence of a stationary distribution is pointed out under certain parametric restrictions. All the results are illustrated by the computer simulations.

KW - stochastic prey-predator model

KW - Brownian motion

KW - extinction

KW - ultimate boundedness

KW - stationary distribution

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DO - 10.1016/j.apm.2018.07.034

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VL - 64

SP - 357

EP - 371

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

ER -

Stochastic prey-predator system with foraging arena scheme

Abstract

Keywords

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Projects

Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)

Long-time dynamics of numerical solutions of stochastic differential equations

Numerical Analysis of Stochastic Differential Equations: New Challenges

Cite this