On temporal and spatial structure in model systems and application to ecological patchiness

  • Daniel M. Dubois
Environment And Pollution
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 2)


Conceptual subdivision of a real system into interacting sub-systems is subjective and is always made with the purpose of explaining a particular phenomenon.

A model system can be represented by a set of partial differential equations the solutions of which simulating self-sustained oscillations and spontaneous spatial structure (morphogenesis).

A class of such model systems, presented in the literature, represents in fact forced temporal and spatial structures due to symmetry breaking of boundary condition.

The general problem dealing with non-homogeneous spatial pattern (patchiness effect) is of great interest in ecological populations in interaction with their stochastic environment. Attention was focused on the mathematical modelling of the mechanism of patches emergence occuring in diffusive predator-prey ecosystems.


Sustained Oscillation Input Flux Homogeneous Steady State Herbivorous Zooplankton Diffusive Instability 
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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Daniel M. Dubois
    • 1
  1. 1.Depts. of Applied Statistics and Operations ResearchUniversity of LIEGE Institute of MathematicsLiegeBelgium

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