Transient periodicity and episodic predictability in biological dynamics

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

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

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
Volume10
Issue number4
DOIs
StatePublished - 1993

Fingerprint

Predictability
Periodicity
periodicity
Saddle
Biological Phenomena
Chaotic systems
Invariant Set
Chaotic System
Forecast
Forecasting
Well-defined
Attractor
Time series
trajectory
Trajectories
Organizations
time series
Trajectory
Motion

Keywords

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

ASJC Scopus subject areas

  • Pharmacology
  • Neuroscience(all)
  • Immunology and Microbiology(all)
  • Environmental Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Modeling and Simulation
  • Applied Mathematics

Cite this

Transient periodicity and episodic predictability in biological dynamics. / Schaffer, William M; Kendall, B. E.; Tidd, C. W.; Olsen, L. F.

In: Mathematical Medicine and Biology, Vol. 10, No. 4, 1993, p. 227-247.

Research output: Contribution to journalArticle

Schaffer, William M ; Kendall, B. E. ; Tidd, C. W. ; Olsen, L. F. / Transient periodicity and episodic predictability in biological dynamics. In: Mathematical Medicine and Biology. 1993 ; Vol. 10, No. 4. pp. 227-247.
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