Basins of attraction

Population dynamics with two stable 4-cycles

Shandelle M. Henson, Robert F Costantino, Robert A. Desharnais, Jim M Cushing, Brian Dennis

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We use the concepts of composite maps, basins of attraction, basin switching, and saddle fly-by's to make the ecological hypothesis of the existence of multiple attractors more accessible to experimental scrutiny. Specifically, in a periodically forced insect population growth model we identify multiple attractors, namely, two locally stable 4-cycles. Using the model-predicted basins of attraction, we examine data time series from a Tribolium experiment for evidence of the multiple attractors. We conclude that the multiple attractor hypothesis together with demographic stochasticity accounts for the experimental observations.

Original languageEnglish (US)
Pages (from-to)17-24
Number of pages8
JournalOikos
Volume98
Issue number1
DOIs
StatePublished - 2002

Fingerprint

population dynamics
basins
basin
saddles
stochasticity
growth models
time series analysis
population growth
demographic statistics
insect
time series
insects
experiment

ASJC Scopus subject areas

  • Ecology

Cite this

Basins of attraction : Population dynamics with two stable 4-cycles. / Henson, Shandelle M.; Costantino, Robert F; Desharnais, Robert A.; Cushing, Jim M; Dennis, Brian.

In: Oikos, Vol. 98, No. 1, 2002, p. 17-24.

Research output: Contribution to journalArticle

Henson, Shandelle M. ; Costantino, Robert F ; Desharnais, Robert A. ; Cushing, Jim M ; Dennis, Brian. / Basins of attraction : Population dynamics with two stable 4-cycles. In: Oikos. 2002 ; Vol. 98, No. 1. pp. 17-24.
@article{10fb3ceb438e420f94f71f2a12dc7661,
title = "Basins of attraction: Population dynamics with two stable 4-cycles",
abstract = "We use the concepts of composite maps, basins of attraction, basin switching, and saddle fly-by's to make the ecological hypothesis of the existence of multiple attractors more accessible to experimental scrutiny. Specifically, in a periodically forced insect population growth model we identify multiple attractors, namely, two locally stable 4-cycles. Using the model-predicted basins of attraction, we examine data time series from a Tribolium experiment for evidence of the multiple attractors. We conclude that the multiple attractor hypothesis together with demographic stochasticity accounts for the experimental observations.",
author = "Henson, {Shandelle M.} and Costantino, {Robert F} and Desharnais, {Robert A.} and Cushing, {Jim M} and Brian Dennis",
year = "2002",
doi = "10.1034/j.1600-0706.2002.980102.x",
language = "English (US)",
volume = "98",
pages = "17--24",
journal = "Oikos",
issn = "0030-1299",
publisher = "Wiley-Blackwell",
number = "1",

}

TY - JOUR

T1 - Basins of attraction

T2 - Population dynamics with two stable 4-cycles

AU - Henson, Shandelle M.

AU - Costantino, Robert F

AU - Desharnais, Robert A.

AU - Cushing, Jim M

AU - Dennis, Brian

PY - 2002

Y1 - 2002

N2 - We use the concepts of composite maps, basins of attraction, basin switching, and saddle fly-by's to make the ecological hypothesis of the existence of multiple attractors more accessible to experimental scrutiny. Specifically, in a periodically forced insect population growth model we identify multiple attractors, namely, two locally stable 4-cycles. Using the model-predicted basins of attraction, we examine data time series from a Tribolium experiment for evidence of the multiple attractors. We conclude that the multiple attractor hypothesis together with demographic stochasticity accounts for the experimental observations.

AB - We use the concepts of composite maps, basins of attraction, basin switching, and saddle fly-by's to make the ecological hypothesis of the existence of multiple attractors more accessible to experimental scrutiny. Specifically, in a periodically forced insect population growth model we identify multiple attractors, namely, two locally stable 4-cycles. Using the model-predicted basins of attraction, we examine data time series from a Tribolium experiment for evidence of the multiple attractors. We conclude that the multiple attractor hypothesis together with demographic stochasticity accounts for the experimental observations.

UR - http://www.scopus.com/inward/record.url?scp=0036342957&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036342957&partnerID=8YFLogxK

U2 - 10.1034/j.1600-0706.2002.980102.x

DO - 10.1034/j.1600-0706.2002.980102.x

M3 - Article

VL - 98

SP - 17

EP - 24

JO - Oikos

JF - Oikos

SN - 0030-1299

IS - 1

ER -