Multiple attractors, saddles, and population dynamics in periodic habitats

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

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

Mathematical models predict that a population which oscillates in the absence of time-dependent factors can develop multiple attracting final states in the advent of periodic forcing. A periodically-forced, stage- structured mathematical model predicted the transient and asymptotic behaviors of Tribolium (flour beetle) populations cultured in periodic habitats of fluctuating flour volume. Predictions included multiple (2-cycle) attractors, resonance and attenuation phenomena, and saddle influences. Stochasticity, combined with the deterministic effects of an unstable 'saddle cycle' separating the two stable cycles, is used to explain the observed transients and final states of the experimental cultures. In experimental regimes containing multiple attractors, the presence of unstable invariant sets, as well as stochasticity and the nature, location, and size of basins of attraction, are all central to the interpretation of data.

Original languageEnglish (US)
Pages (from-to)1121-1149
Number of pages29
JournalBulletin of Mathematical Biology
Volume61
Issue number6
DOIs
StatePublished - Oct 1999

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Population dynamics
saddles
Population Dynamics
Flour
Saddle
stochasticity
Ecosystem
Attractor
population dynamics
Theoretical Models
mathematical models
Stochasticity
experimental culture
Tribolium
Mathematical models
Tribolium (Coleoptera)
Cycle
Tenebrionidae
Beetles
habitat

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this

Multiple attractors, saddles, and population dynamics in periodic habitats. / Henson, Shandelle M.; Costantino, Robert F; Cushing, Jim M; Dennis, Brian; Desharnais, Robert A.

In: Bulletin of Mathematical Biology, Vol. 61, No. 6, 10.1999, p. 1121-1149.

Research output: Contribution to journalArticle

Henson, Shandelle M. ; Costantino, Robert F ; Cushing, Jim M ; Dennis, Brian ; Desharnais, Robert A. / Multiple attractors, saddles, and population dynamics in periodic habitats. In: Bulletin of Mathematical Biology. 1999 ; Vol. 61, No. 6. pp. 1121-1149.
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