Chaotic behavior of three competing species of May-Leonard model under small periodic perturbations

Valentin S. Afraimovich, Sze Bi Hsu, Huey Er Lin

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The influence of periodic perturbations to a Lotka-Volterra system, modeling a competition between three species, is studied, provided that in the unperturbed case the system has a unique attractor - a contour of heteroclinic orbits joining unstable equilibria. It is shown that the perturbed system may manifest regular behavior corresponding to the existence of a smooth invariant torus, and, as well, may have chaotic regimes depending on some parameters. Theoretical results are confirmed by numerical simulations.

Original languageEnglish
Pages (from-to)435-447
Number of pages13
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume11
Issue number2
DOIs
Publication statusPublished - 2001 Feb

Fingerprint

Competing Species
Heteroclinic Orbit
Invariant Tori
Lotka-Volterra System
Perturbed System
Chaotic Behavior
Joining
System Modeling
Attractor
Orbits
Unstable
Perturbation
Numerical Simulation
Computer simulation
Model
Influence

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

Cite this

Chaotic behavior of three competing species of May-Leonard model under small periodic perturbations. / Afraimovich, Valentin S.; Hsu, Sze Bi; Lin, Huey Er.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 11, No. 2, 02.2001, p. 435-447.

Research output: Contribution to journalArticle

@article{31f22edab5814947b7df807c6f58a170,
title = "Chaotic behavior of three competing species of May-Leonard model under small periodic perturbations",
abstract = "The influence of periodic perturbations to a Lotka-Volterra system, modeling a competition between three species, is studied, provided that in the unperturbed case the system has a unique attractor - a contour of heteroclinic orbits joining unstable equilibria. It is shown that the perturbed system may manifest regular behavior corresponding to the existence of a smooth invariant torus, and, as well, may have chaotic regimes depending on some parameters. Theoretical results are confirmed by numerical simulations.",
author = "Afraimovich, {Valentin S.} and Hsu, {Sze Bi} and Lin, {Huey Er}",
year = "2001",
month = "2",
doi = "10.1142/S021812740100216X",
language = "English",
volume = "11",
pages = "435--447",
journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",
issn = "0218-1274",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",

}

TY - JOUR

T1 - Chaotic behavior of three competing species of May-Leonard model under small periodic perturbations

AU - Afraimovich, Valentin S.

AU - Hsu, Sze Bi

AU - Lin, Huey Er

PY - 2001/2

Y1 - 2001/2

N2 - The influence of periodic perturbations to a Lotka-Volterra system, modeling a competition between three species, is studied, provided that in the unperturbed case the system has a unique attractor - a contour of heteroclinic orbits joining unstable equilibria. It is shown that the perturbed system may manifest regular behavior corresponding to the existence of a smooth invariant torus, and, as well, may have chaotic regimes depending on some parameters. Theoretical results are confirmed by numerical simulations.

AB - The influence of periodic perturbations to a Lotka-Volterra system, modeling a competition between three species, is studied, provided that in the unperturbed case the system has a unique attractor - a contour of heteroclinic orbits joining unstable equilibria. It is shown that the perturbed system may manifest regular behavior corresponding to the existence of a smooth invariant torus, and, as well, may have chaotic regimes depending on some parameters. Theoretical results are confirmed by numerical simulations.

UR - http://www.scopus.com/inward/record.url?scp=0035609051&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035609051&partnerID=8YFLogxK

U2 - 10.1142/S021812740100216X

DO - 10.1142/S021812740100216X

M3 - Article

AN - SCOPUS:0035609051

VL - 11

SP - 435

EP - 447

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 2

ER -