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Complex discrete dynamics from simple continuous population models.

Javier G P Gamarra1, Ricard V Solé

  • 1Complex Systems Research Group, Department of Physics FEN, Universitat Politècnica de Catalunya, Campus Nord, Mòdul B4-B5, 08034 Barcelona, Spain. javier@complex.upc.es

Bulletin of Mathematical Biology
|July 4, 2002
PubMed
Summary

This study models population dynamics using a hybrid approach, combining continuous processes with discrete reproduction events. The model

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Area of Science:

  • Population Dynamics and Mathematical Ecology
  • Ecological Modeling
  • Chaos Theory in Ecology

Background:

  • Classical population models often use difference equations for discrete generations.
  • Ecological processes like resource consumption and mortality occur continuously within generations.
  • Integrating continuous and discrete events in population modeling presents a challenge.

Purpose of the Study:

  • To develop a more realistic hybrid model for population dynamics.
  • To investigate the dynamics of a system with continuous resource-consumer interactions and discrete reproduction.
  • To explore the emergence of complex dynamics, including chaos, in this hybrid model.

Main Methods:

  • Developed a hybrid ordinary differential equation (ODE) bidimensional model.

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  • Incorporated discrete events for reproduction within the continuous model framework.
  • Employed numerical and analytical approaches to study the model's dynamics.
  • Conducted stochastic simulations to assess the impact of specific parameters.

    • Main Results:

    • The hybrid model's dynamics closely resemble the Ricker map.
    • The model exhibits a 'doubling route to chaos', a known pathway to complex population fluctuations.
    • Stochastic simulations indicate that handling time in juvenile competition can alter the model's qualitative behavior.

    Conclusions:

    • Hybrid models offer a more realistic representation of population dynamics by integrating continuous and discrete processes.
    • The Ricker map-like dynamics and route to chaos highlight the potential for complex population behavior even in simplified hybrid models.
    • Further research into the effects of stochasticity and specific ecological parameters like handling time is warranted.