Bulletin of Mathematical Biology

, Volume 54, Issue 4, pp 619–648 | Cite as

Complex dynamics in a model microbial system

  • Mark Kot
  • Gary S. Sayler
  • Terry W. Schultz
Article

Abstract

The forced double-Monod model (for a chemostat with a predator, a prey and periodically forced inflowing substrate) displays quasiperiodicity, phase locking, period doubling and chaotic dynamics. Stroboscopic sections reveal circle maps for the quasiperiodic regimes and noninvertible maps of the interval for the chaotic regimes. Criticality in the circle maps sets the stage for chaos in the model. This criticality may arise with an increase in the period or amplitude of forcing.

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Copyright information

© Society for Mathematical Biology 1992

Authors and Affiliations

  • Mark Kot
    • 1
  • Gary S. Sayler
    • 2
  • Terry W. Schultz
    • 3
  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of Animal Science-Veterinary MedicineUniversity of TennesseeKnoxvilleUSA
  3. 3.Department of Animal Science-Veterinary MedicineUniversity of TennesseeKnoxvilleUSA

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