Journal of Statistical Physics

, Volume 81, Issue 3–4, pp 761–775 | Cite as

Anomalous biennial oscillations in a Fisher equation with a discretized verhulst term

  • C. Walsh
  • T. S. Ray
  • Naeem Jan


The dynamics of a biological population governed by a modified Fisher equation is studied by means of Monte Carlo simulations. Reproduction of the population occurs at discrete times, while transport caused by diffusion and conduction takes place on shorter time scales. The discrete reproduction, modeled with a set of coupled logistic maps, exhibits phenomena which are not evident in the usual continuum version of the Fisher equation. Several mechanisms for biennial oscillations of the total population are investigated. One of these shows an ordered coupling between random diffusive motion and the chaotic attractor of the logistic map.

Key Words

Logistic map diffusion Fisher equation chaos oscillations 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • C. Walsh
    • 1
  • T. S. Ray
    • 1
    • 2
  • Naeem Jan
    • 1
  1. 1.Department of PhysicsSt. Francis Xavier UniversityAntigonishCanada
  2. 2.Division of ScienceNortheast Missouri State UniversityKirksville

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