Mathematical modeling of cyclic population dynamics

Alvin Bayliss; A. A. Nepomnyashchy; Vladimir Volpert

doi:10.1016/j.physd.2019.01.010

Mathematical modeling of cyclic population dynamics

Alvin Bayliss^*, A. A. Nepomnyashchy, Vladimir Volpert

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

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

2 Scopus citations

Abstract

A rock–paper–scissors three species cyclic ecosystem is considered. Deterministic mathematical models based on delayed ODEs and nonlocal PDEs are proposed and studied both analytically and numerically. Transitions between the coexistence state that is associated with biodiversity, limit cycles and the heteroclinic cycle are discussed for the ODE model. Traveling waves between the coexistence state and single species states are studied for the PDE model. We show that delay promotes oscillatory instabilities of the coexistence state while nonlocality promotes stationary cellular instabilities.

Original language	English (US)
Journal	Physica D: Nonlinear Phenomena
DOIs	https://doi.org/10.1016/j.physd.2019.01.010
State	Published - Jan 1 2019

Keywords

Cyclic ecosystems
Delay equations
Heteroclinic cycle
Nonlocality
Population dynamics
Traveling wave

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Condensed Matter Physics

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10.1016/j.physd.2019.01.010

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title = "Mathematical modeling of cyclic population dynamics",

abstract = "A rock–paper–scissors three species cyclic ecosystem is considered. Deterministic mathematical models based on delayed ODEs and nonlocal PDEs are proposed and studied both analytically and numerically. Transitions between the coexistence state that is associated with biodiversity, limit cycles and the heteroclinic cycle are discussed for the ODE model. Traveling waves between the coexistence state and single species states are studied for the PDE model. We show that delay promotes oscillatory instabilities of the coexistence state while nonlocality promotes stationary cellular instabilities.",

keywords = "Cyclic ecosystems, Delay equations, Heteroclinic cycle, Nonlocality, Population dynamics, Traveling wave",

author = "Alvin Bayliss and Nepomnyashchy, {A. A.} and Vladimir Volpert",

year = "2019",

month = jan,

day = "1",

doi = "10.1016/j.physd.2019.01.010",

language = "English (US)",

journal = "Physica D: Nonlinear Phenomena",

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TY - JOUR

T1 - Mathematical modeling of cyclic population dynamics

AU - Bayliss, Alvin

AU - Nepomnyashchy, A. A.

AU - Volpert, Vladimir

PY - 2019/1/1

Y1 - 2019/1/1

N2 - A rock–paper–scissors three species cyclic ecosystem is considered. Deterministic mathematical models based on delayed ODEs and nonlocal PDEs are proposed and studied both analytically and numerically. Transitions between the coexistence state that is associated with biodiversity, limit cycles and the heteroclinic cycle are discussed for the ODE model. Traveling waves between the coexistence state and single species states are studied for the PDE model. We show that delay promotes oscillatory instabilities of the coexistence state while nonlocality promotes stationary cellular instabilities.

AB - A rock–paper–scissors three species cyclic ecosystem is considered. Deterministic mathematical models based on delayed ODEs and nonlocal PDEs are proposed and studied both analytically and numerically. Transitions between the coexistence state that is associated with biodiversity, limit cycles and the heteroclinic cycle are discussed for the ODE model. Traveling waves between the coexistence state and single species states are studied for the PDE model. We show that delay promotes oscillatory instabilities of the coexistence state while nonlocality promotes stationary cellular instabilities.

KW - Cyclic ecosystems

KW - Delay equations

KW - Heteroclinic cycle

KW - Nonlocality

KW - Population dynamics

KW - Traveling wave

UR - http://www.scopus.com/inward/record.url?scp=85062811085&partnerID=8YFLogxK

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U2 - 10.1016/j.physd.2019.01.010

DO - 10.1016/j.physd.2019.01.010

M3 - Article

AN - SCOPUS:85062811085

SN - 0167-2789

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

ER -

Mathematical modeling of cyclic population dynamics

Abstract

Keywords

ASJC Scopus subject areas

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