Moving toward an unstable equilibrium: Saddle nodes in population systems

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

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


1. We identify an unstable equilibrium with a two-dimensional stable manifold and a one-dimensional unstable manifold in a three-state variable (larva, pupa, adult) insect population growth model. 2. The saddle node forecasts that the time series of some initial numbers of larvae, pupae and adults are drawn closely to the unstable equilibrium before approaching the asymptotic stable attractor (a two-cycle), while the time series of other initial points are not. 3. Using two quantitative indices, we examine time series from a Tribolium experiment for evidence of the predicted saddle node. We conclude that a saddle node accounts for the transient dynamics in these data and for the differences between the transient behaviour of different replicates of the same experiment.

Original languageEnglish (US)
Pages (from-to)298-306
Number of pages9
JournalJournal of Animal Ecology
Issue number2
StatePublished - Mar 1998


  • Non-linear demographic dynamics
  • Transient behaviour
  • Tribolium

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Animal Science and Zoology


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