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Monitoring and Control in a Spatially Structured Population Model

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Book cover Computational Science and Its Applications - ICCSA 2011 (ICCSA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6786))

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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.

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Author information

Authors and Affiliations

  1. Department of Statistics and Applied Mathematics, University of Almería, La Cañada de San Urbano, 04120, Almería, Spain

    Manuel Gámez & Inmaculada López

  2. Research Group of Theoretical Biology and Ecological Modelling, of Hungarian Academy of Science and, Department of Plant Taxonomy and Ecology, L. Eotvos University, Pázmány P. st1/c, H-1117, Budapest, Hungary

    József Garay

  3. Institute of Mathematics and Informatics, Szent István University, Páter K. u. 1., H-2103, Godollo, Hungary

    Zoltán Varga

Authors
  1. Manuel Gámez
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  2. Inmaculada López
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  3. József Garay
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  4. Zoltán Varga
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Editor information

Editors and Affiliations

  1. L.I.S.U.T. - D.A.P.I.T., Basilicata University Potenza, 10, Viale dell’Ateneo Lucano, 85100, Potenza, Italy

    Beniamino Murgante

  2. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

  3. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros, s/n, C.P. 39005, Santander, Spain

    Andrés Iglesias

  4. School of Business Systems, Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  5. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, Higashi-ku, 813-8503, Fukuoka, Japan

    Bernady O. Apduhan

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© 2011 Springer-Verlag Berlin Heidelberg

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Gámez, M., López, I., Garay, J., Varga, Z. (2011). Monitoring and Control in a Spatially Structured Population Model. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications - ICCSA 2011. ICCSA 2011. Lecture Notes in Computer Science, vol 6786. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21934-4_41

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  • DOI: https://doi.org/10.1007/978-3-642-21934-4_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21933-7

  • Online ISBN: 978-3-642-21934-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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