Food chain chaos due to Shilnikov's orbit

Bo Deng; Gwendolen Hines

doi:10.1063/1.1482255

Food chain chaos due to Shilnikov's orbit

Bo Deng, Gwendolen Hines

Mathematics

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

53 Scopus citations

Abstract

Assume that the reproduction rate ratio ζ of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption translates the model into a singularly perturbed system of two time scales. It is demonstrated, as a sequel to the earlier paper of Deng [Chaos 11, 514-525 (2001)], that at the singular limit ζ=0, a singular Shilnikov's saddle-focus homoclinic orbit can exist as the reproduction rate ratio e of the top-predator over the predator is greater than a modest value ε₀. The additional conditions under which such a singular orbit may occur are also explicitly given.

Original language	English (US)
Pages (from-to)	533-538
Number of pages	6
Journal	Chaos
Volume	12
Issue number	3
DOIs	https://doi.org/10.1063/1.1482255
State	Published - Sep 2002

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

Access to Document

10.1063/1.1482255

Cite this

@article{6f19ee70872149a7b15a0746633760c5,

title = "Food chain chaos due to Shilnikov's orbit",

abstract = "Assume that the reproduction rate ratio ζ of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption translates the model into a singularly perturbed system of two time scales. It is demonstrated, as a sequel to the earlier paper of Deng [Chaos 11, 514-525 (2001)], that at the singular limit ζ=0, a singular Shilnikov's saddle-focus homoclinic orbit can exist as the reproduction rate ratio e of the top-predator over the predator is greater than a modest value ε0. The additional conditions under which such a singular orbit may occur are also explicitly given.",

author = "Bo Deng and Gwendolen Hines",

year = "2002",

month = sep,

doi = "10.1063/1.1482255",

language = "English (US)",

volume = "12",

pages = "533--538",

journal = "Chaos",

issn = "1054-1500",

publisher = "American Institute of Physics Publising LLC",

number = "3",

}

TY - JOUR

T1 - Food chain chaos due to Shilnikov's orbit

AU - Deng, Bo

AU - Hines, Gwendolen

PY - 2002/9

Y1 - 2002/9

N2 - Assume that the reproduction rate ratio ζ of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption translates the model into a singularly perturbed system of two time scales. It is demonstrated, as a sequel to the earlier paper of Deng [Chaos 11, 514-525 (2001)], that at the singular limit ζ=0, a singular Shilnikov's saddle-focus homoclinic orbit can exist as the reproduction rate ratio e of the top-predator over the predator is greater than a modest value ε0. The additional conditions under which such a singular orbit may occur are also explicitly given.

AB - Assume that the reproduction rate ratio ζ of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption translates the model into a singularly perturbed system of two time scales. It is demonstrated, as a sequel to the earlier paper of Deng [Chaos 11, 514-525 (2001)], that at the singular limit ζ=0, a singular Shilnikov's saddle-focus homoclinic orbit can exist as the reproduction rate ratio e of the top-predator over the predator is greater than a modest value ε0. The additional conditions under which such a singular orbit may occur are also explicitly given.

UR - http://www.scopus.com/inward/record.url?scp=0036710119&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036710119&partnerID=8YFLogxK

U2 - 10.1063/1.1482255

DO - 10.1063/1.1482255

M3 - Article

C2 - 12779583

AN - SCOPUS:0036710119

VL - 12

SP - 533

EP - 538

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 3

ER -

Food chain chaos due to Shilnikov's orbit

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this