Multiple attractors, saddles, and population dynamics in periodic habitats

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

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


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
Issue number6
StatePublished - Oct 1999

ASJC Scopus subject areas

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics


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