Bulletin of Mathematical Biology

, Volume 64, Issue 3, pp 611–620

Complex discrete dynamics from simple continuous population models

  • Javier G. P. Gamarra
  • Ricard V. Solé
Article

DOI: 10.1006/bulm.2002.0286

Cite this article as:
Gamarra, J.G.P. & Solé, R.V. Bull. Math. Biol. (2002) 64: 611. doi:10.1006/bulm.2002.0286

Abstract

Nonoverlapping generations have been classically modelled as difference equations in order to account for the discrete nature of reproductive events. However, other events such as resource consumption or mortality are continuous and take place in the within-generation time. We have realistically assumed a hybrid ODE bidimensional model of resources and consumers with discrete events for reproduction. Numerical and analytical approaches showed that the resulting dynamics resembles a Ricker map, including the doubling route to chaos. Stochastic simulations with a handling-time parameter for indirect competition of juveniles may affect the qualitative behaviour of the model.

Copyright information

© Society for Mathematical Biology 2002

Authors and Affiliations

  • Javier G. P. Gamarra
    • 1
  • Ricard V. Solé
    • 1
    • 2
  1. 1.Complex Systems Research Group, Department of Physics FENUniversitat Politècnica de Catalunya, Campus Nord, Mòdul B4-B5BarcelonaSpain
  2. 2.Santa Fe InstituteSanta FeUSA