Transient periodicity and episodic predictability in biological dynamics

W. M. Schaffer, B. E. Kendall, C. W. Tidd, L. F. Olsen

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


Biological time series often contain passing episodes of nearly periodic dynamics. In chaotic systems, such transient periodicity can reflect the existence of semiperiodic saddles-nonstable invariant sets-contained in the attractor. Motion in the vicinity of such objects has a prominent periodic component. In addition, trajectories can become temporarily trapped in these neighbourhoods before exiting. The immediate dynamical antecedents (low-order preimages) of transient periodicity are well defined and, along with the saddles to which they map, correspond to regions of enhanced predictability under nonlinear forecasting. This suggests that it may be possible to forecast the onset of transient periodicity in systems for which overall predictability is low. The present paper reviews these concepts and applies them to biological phenomena at different levels of organization.

Original languageEnglish (US)
Pages (from-to)227-247
Number of pages21
JournalMathematical Medicine and Biology
Issue number4
StatePublished - 1993


  • Chaos
  • Epidemiology
  • Epilepsy
  • Nonlinear forecasting
  • SEIR model
  • Semiattractors
  • Transient periodicity

ASJC Scopus subject areas

  • General Medicine


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