On the exponentially self-regulating population model

Jerry Chen, Denis Blackmore

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


A new type of discrete dynamical systems model for populations, called an exponentially self-regulating (ESR) map, is introduced and analyzed in considerable detail for the case of two competing species. The ESR model exhibits many dynamical features consistent with the observed interactions of populations and subsumes some of the most successful discrete biological models that have been studied in the literature. For example, the well-known Tribolium model is an ESR map. It is shown that in addition to logistic dynamics - ranging from the very simple to manifestly chaotic one-dimensional regimes - the ESR model exhibits, for some parameter values, its own brands of bifurcation and chaos that are essentially two-dimensional in nature. In particular, it is proved that ESR systems have twisted horseshoe with bending tail dynamics associated to an essentially global strange attractor for certain parameter ranges. The existence of a global strange attractor makes the ESR map more plausible as a model for actual populations than several other extant models, including the Lotka-Volterra map.

Original languageEnglish (US)
Pages (from-to)1433-1450
Number of pages18
JournalChaos, Solitons and Fractals
Issue number9
StatePublished - Dec 2002

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Mathematics
  • General Physics and Astronomy
  • Applied Mathematics


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