Multiple mixed-type attractors in a competition model

J. M. Cushing; Shandelle M. Henson; Chantel C. Blackburn

doi:10.1080/17513750701610010

Multiple mixed-type attractors in a competition model

J. M. Cushing, Shandelle M. Henson, Chantel C. Blackburn

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

75 Scopus citations

Abstract

We show that a discrete-time, two-species competition model with Ricker (exponential) nonlinearities can exhibit multiple mixed-type attractors. By this is meant dynamic scenarios in which there are simultaneously present both coexistence attractors (in which both species are present) and exclusion attractors (in which one species is absent). Recent studies have investigated the inclusion of life-cycle stages in competition models as a casual mechanism for the existence of these kinds of multiple attractors. In this paper we investigate the role of nonlinearities in competition models without life-cycle stages.

Original language	English (US)
Pages (from-to)	347-362
Number of pages	16
Journal	Journal of biological dynamics
Volume	1
Issue number	4
DOIs	https://doi.org/10.1080/17513750701610010
State	Published - Oct 2007
Externally published	Yes

Keywords

Coexistence cycles
Competitive exclusion principle
Multiple attractors

ASJC Scopus subject areas

Ecology, Evolution, Behavior and Systematics
Ecology

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10.1080/17513750701610010

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title = "Multiple mixed-type attractors in a competition model",

abstract = "We show that a discrete-time, two-species competition model with Ricker (exponential) nonlinearities can exhibit multiple mixed-type attractors. By this is meant dynamic scenarios in which there are simultaneously present both coexistence attractors (in which both species are present) and exclusion attractors (in which one species is absent). Recent studies have investigated the inclusion of life-cycle stages in competition models as a casual mechanism for the existence of these kinds of multiple attractors. In this paper we investigate the role of nonlinearities in competition models without life-cycle stages.",

keywords = "Coexistence cycles, Competitive exclusion principle, Multiple attractors",

author = "Cushing, {J. M.} and Henson, {Shandelle M.} and Blackburn, {Chantel C.}",

note = "Funding Information: We thank R.F. Constantino, J. Edmunds, S.L. Robertson and S. Arpin for helpful discussions. J.M. Cushing and S.M. Henson were supported in part by NSF grant DMS-0414142.",

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T1 - Multiple mixed-type attractors in a competition model

AU - Cushing, J. M.

AU - Henson, Shandelle M.

AU - Blackburn, Chantel C.

N1 - Funding Information: We thank R.F. Constantino, J. Edmunds, S.L. Robertson and S. Arpin for helpful discussions. J.M. Cushing and S.M. Henson were supported in part by NSF grant DMS-0414142.

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Y1 - 2007/10

N2 - We show that a discrete-time, two-species competition model with Ricker (exponential) nonlinearities can exhibit multiple mixed-type attractors. By this is meant dynamic scenarios in which there are simultaneously present both coexistence attractors (in which both species are present) and exclusion attractors (in which one species is absent). Recent studies have investigated the inclusion of life-cycle stages in competition models as a casual mechanism for the existence of these kinds of multiple attractors. In this paper we investigate the role of nonlinearities in competition models without life-cycle stages.

AB - We show that a discrete-time, two-species competition model with Ricker (exponential) nonlinearities can exhibit multiple mixed-type attractors. By this is meant dynamic scenarios in which there are simultaneously present both coexistence attractors (in which both species are present) and exclusion attractors (in which one species is absent). Recent studies have investigated the inclusion of life-cycle stages in competition models as a casual mechanism for the existence of these kinds of multiple attractors. In this paper we investigate the role of nonlinearities in competition models without life-cycle stages.

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KW - Competitive exclusion principle

KW - Multiple attractors

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Multiple mixed-type attractors in a competition model

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Keywords

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