Effect of a functional response-dependent prey refuge in a predator–prey model

Mainul Haque; Md Sabiar Rahman; Ezio Venturino; Bai-lian Li

doi:10.1016/j.ecocom.2014.04.001

Effect of a functional response-dependent prey refuge in a predator–prey model

Mainul Haque, Md Sabiar Rahman, Ezio Venturino, Bai-lian Li

School of Mathematics & Physics

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

Abstract

We propose two mathematical models for predator–prey interactions allowing for prey refuge. The novelty lies in the assumption that the amount of prey in refugia is proportional not only to the encounters between prey and predator, but also it is modelled by a Holling type II response function. The second model also accounts for predator's intraspecific competition. We fully analyse the models and discuss all possible coexistence equilibria configurations and their local and global stability. A saddle-node bifurcation analysis is also performed for a wide set of parameter ranges. The ultimate behavior of the systems depends mainly on two relevant parameters, the prey refuge constant and the predator's intraspecific competition.

Original language	English
Pages (from-to)	248-256
Journal	Ecological Complexity
Volume	20
Early online date	7 Aug 2014
DOIs	https://doi.org/10.1016/j.ecocom.2014.04.001
Publication status	Published - 1 Dec 2014

Keywords

RCUK
EPSRC

Access to Document

10.1016/j.ecocom.2014.04.001

https://linkinghub.elsevier.com/retrieve/pii/S1476945X14000324

Cite this

@article{f63d052d2a294b1fb758cd3c0bd6857f,

title = "Effect of a functional response-dependent prey refuge in a predator–prey model",

abstract = "We propose two mathematical models for predator–prey interactions allowing for prey refuge. The novelty lies in the assumption that the amount of prey in refugia is proportional not only to the encounters between prey and predator, but also it is modelled by a Holling type II response function. The second model also accounts for predator's intraspecific competition. We fully analyse the models and discuss all possible coexistence equilibria configurations and their local and global stability. A saddle-node bifurcation analysis is also performed for a wide set of parameter ranges. The ultimate behavior of the systems depends mainly on two relevant parameters, the prey refuge constant and the predator's intraspecific competition.",

keywords = "RCUK, EPSRC",

author = "Mainul Haque and Rahman, {Md Sabiar} and Ezio Venturino and Bai-lian Li",

note = "Post-print unavailable.",

year = "2014",

month = dec,

day = "1",

doi = "10.1016/j.ecocom.2014.04.001",

language = "English",

volume = "20",

pages = "248--256",

journal = "Ecological Complexity",

issn = "1476-945X",

publisher = "Elsevier",

}

TY - JOUR

T1 - Effect of a functional response-dependent prey refuge in a predator–prey model

AU - Haque, Mainul

AU - Rahman, Md Sabiar

AU - Venturino, Ezio

AU - Li, Bai-lian

N1 - Post-print unavailable.

PY - 2014/12/1

Y1 - 2014/12/1

N2 - We propose two mathematical models for predator–prey interactions allowing for prey refuge. The novelty lies in the assumption that the amount of prey in refugia is proportional not only to the encounters between prey and predator, but also it is modelled by a Holling type II response function. The second model also accounts for predator's intraspecific competition. We fully analyse the models and discuss all possible coexistence equilibria configurations and their local and global stability. A saddle-node bifurcation analysis is also performed for a wide set of parameter ranges. The ultimate behavior of the systems depends mainly on two relevant parameters, the prey refuge constant and the predator's intraspecific competition.

AB - We propose two mathematical models for predator–prey interactions allowing for prey refuge. The novelty lies in the assumption that the amount of prey in refugia is proportional not only to the encounters between prey and predator, but also it is modelled by a Holling type II response function. The second model also accounts for predator's intraspecific competition. We fully analyse the models and discuss all possible coexistence equilibria configurations and their local and global stability. A saddle-node bifurcation analysis is also performed for a wide set of parameter ranges. The ultimate behavior of the systems depends mainly on two relevant parameters, the prey refuge constant and the predator's intraspecific competition.

KW - RCUK

KW - EPSRC

U2 - 10.1016/j.ecocom.2014.04.001

DO - 10.1016/j.ecocom.2014.04.001

M3 - Article

SN - 1476-945X

VL - 20

SP - 248

EP - 256

JO - Ecological Complexity

JF - Ecological Complexity

ER -

Effect of a functional response-dependent prey refuge in a predator–prey model

Abstract

Keywords

Access to Document

Fingerprint

Cite this