The effect of the remains of the carcass in a two-prey, one-predator model

Sungrim Seirin Lee, Tsuyoshi Kajiwara

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We propose a two-prey, one-predator model involving the effect of the carcass. We consider a commensal interaction that a prey species eats the remains of the other prey species' carcass given by their predator. Under some biological assumptions, we construct two ODE models. We analyze the linear stability and prove the permanence of the two models. We also show that the effect of the remains of the carcass leads to chaotic dynamics for biologically reasonable choices of parameters by numerical simulations. Finally, we discuss the dynamical results and the coexistent regions of the three species.

Original languageEnglish
Pages (from-to)353-374
Number of pages22
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume9
Issue number2
Publication statusPublished - Mar 2008

Fingerprint

Predator
Prey
Permanence
Chaotic Dynamics
Linear Stability
Model
Numerical Simulation
Computer simulation
Interaction

Keywords

  • Chaos
  • Mathematical modeling
  • Population dynamics

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

The effect of the remains of the carcass in a two-prey, one-predator model. / Lee, Sungrim Seirin; Kajiwara, Tsuyoshi.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 9, No. 2, 03.2008, p. 353-374.

Research output: Contribution to journalArticle

@article{60d8970fd6bd4e67aec154a387f1ed60,
title = "The effect of the remains of the carcass in a two-prey, one-predator model",
abstract = "We propose a two-prey, one-predator model involving the effect of the carcass. We consider a commensal interaction that a prey species eats the remains of the other prey species' carcass given by their predator. Under some biological assumptions, we construct two ODE models. We analyze the linear stability and prove the permanence of the two models. We also show that the effect of the remains of the carcass leads to chaotic dynamics for biologically reasonable choices of parameters by numerical simulations. Finally, we discuss the dynamical results and the coexistent regions of the three species.",
keywords = "Chaos, Mathematical modeling, Population dynamics",
author = "Lee, {Sungrim Seirin} and Tsuyoshi Kajiwara",
year = "2008",
month = "3",
language = "English",
volume = "9",
pages = "353--374",
journal = "Discrete and Continuous Dynamical Systems - Series B",
issn = "1531-3492",
publisher = "Southwest Missouri State University",
number = "2",

}

TY - JOUR

T1 - The effect of the remains of the carcass in a two-prey, one-predator model

AU - Lee, Sungrim Seirin

AU - Kajiwara, Tsuyoshi

PY - 2008/3

Y1 - 2008/3

N2 - We propose a two-prey, one-predator model involving the effect of the carcass. We consider a commensal interaction that a prey species eats the remains of the other prey species' carcass given by their predator. Under some biological assumptions, we construct two ODE models. We analyze the linear stability and prove the permanence of the two models. We also show that the effect of the remains of the carcass leads to chaotic dynamics for biologically reasonable choices of parameters by numerical simulations. Finally, we discuss the dynamical results and the coexistent regions of the three species.

AB - We propose a two-prey, one-predator model involving the effect of the carcass. We consider a commensal interaction that a prey species eats the remains of the other prey species' carcass given by their predator. Under some biological assumptions, we construct two ODE models. We analyze the linear stability and prove the permanence of the two models. We also show that the effect of the remains of the carcass leads to chaotic dynamics for biologically reasonable choices of parameters by numerical simulations. Finally, we discuss the dynamical results and the coexistent regions of the three species.

KW - Chaos

KW - Mathematical modeling

KW - Population dynamics

UR - http://www.scopus.com/inward/record.url?scp=70350643407&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350643407&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:70350643407

VL - 9

SP - 353

EP - 374

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 2

ER -