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

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

doi:10.1142/S021812740100216X

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

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

^*Corresponding author for this work

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

28 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 language	English
Pages (from-to)	435-447
Number of pages	13
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	11
Issue number	2
DOIs	https://doi.org/10.1142/S021812740100216X
Publication status	Published - 2001 Feb
Externally published	Yes

ASJC Scopus subject areas

Modelling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

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10.1142/S021812740100216X

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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\}",

note = "Funding Information: ∗The work was done while the rst author visited National Center of Theoretical Science, Hsinchu, Taiwan in April 1999. yPartially supported by National Council of Science, R.O.C.",

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AU - Hsu, Sze Bi

AU - Lin, Huey Er

N1 - Funding Information: ∗The work was done while the rst author visited National Center of Theoretical Science, Hsinchu, Taiwan in April 1999. yPartially supported by National Council of Science, R.O.C.

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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.

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

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