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Monitoring and Control in a Spatially Structured Population Model

  • Manuel Gámez
  • Inmaculada López
  • József Garay
  • Zoltán Varga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6786)

Abstract

In the paper methods of Mathematical Systems Theory are applied to the dynamical analysis of a harvested population with a reserve area. Although the methodology also applies to rather general spatially structured populations, for a concrete interpretation, we consider a fish population living in a free fishing area and in a reserved area, with migration between them. Using a fishing effort model based on logistic growth in both areas, from the catch, by the construction of an auxiliary system called observer, we dynamically estimate the total fish stock. A similar method also applies to the case of a changing environment, when there is a time-dependent abiotic environmental effect described by an additional exosystem. Furthermore, we also consider the problem of steering the population into a desired new equilibrium. To this end an optimal control problem is set up, which is numerically solved using an optimal control toolbox developed for MatLab.

Keywords

spatially structured population fishing effort model observer system equilibrium control 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Manuel Gámez
    • 1
  • Inmaculada López
    • 1
  • József Garay
    • 2
  • Zoltán Varga
    • 3
  1. 1.Department of Statistics and Applied MathematicsUniversity of AlmeríaAlmeríaSpain
  2. 2.Research Group of Theoretical Biology and Ecological Modelling, of Hungarian Academy of Science and, Department of Plant Taxonomy and EcologyL. Eotvos UniversityBudapestHungary
  3. 3.Institute of Mathematics and InformaticsSzent István UniversityGodolloHungary

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