Stochastic delay foraging arena predator–prey system with Markov switching

Yongmei Cai; Siyang Cai; Xuerong Mao

doi:10.1080/07362994.2019.1679645

Stochastic delay foraging arena predator–prey system with Markov switching

Yongmei Cai, Siyang Cai, Xuerong Mao

Research output: Journal Publication › Article › peer-review

16 Citations (Scopus)

Abstract

In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.

Original language	English
Pages (from-to)	191-212
Number of pages	22
Journal	Stochastic Analysis and Applications
Volume	38
Issue number	2
DOIs	https://doi.org/10.1080/07362994.2019.1679645
Publication status	Published - 3 Mar 2020
Externally published	Yes

Keywords

Brownian motion
Markov chain
Stochastic predator–prey model
time delay
ultimate boundedness

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1080/07362994.2019.1679645

Cite this

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title = "Stochastic delay foraging arena predator–prey system with Markov switching",

abstract = "In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.",

keywords = "Brownian motion, Markov chain, Stochastic predator–prey model, time delay, ultimate boundedness",

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T1 - Stochastic delay foraging arena predator–prey system with Markov switching

AU - Cai, Yongmei

AU - Cai, Siyang

AU - Mao, Xuerong

PY - 2020/3/3

Y1 - 2020/3/3

N2 - In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.

AB - In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.

KW - Brownian motion

KW - Markov chain

KW - Stochastic predator–prey model

KW - time delay

KW - ultimate boundedness

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M3 - Article

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SN - 0736-2994

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SP - 191

EP - 212

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 2

ER -

Stochastic delay foraging arena predator–prey system with Markov switching

Abstract

Keywords

ASJC Scopus subject areas

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