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Monitoring in a Discrete-Time Nonlinear Age-Structured Population Model with Changing Environment

Author

Listed:
  • Inmaculada López

    (Department of Mathematics, University of Almería, La Cañada de San Urbano, 04120 Almería, Spain)

  • Zoltán Varga

    (Department of Mathematics and Modelling, Institute of Mathematics and Basic Science, Hungarian University of Agriculture and Life Sciences, Páter K. u. 1, 2100 Godollo, Hungary)

  • Manuel Gámez

    (Department of Mathematics, University of Almería, La Cañada de San Urbano, 04120 Almería, Spain)

  • József Garay

    (Institute of Evolution, Centre for Ecological Research, Konkoly-Thege Miklós út 29-33, 1121 Budapest, Hungary)

Abstract

This paper is a contribution to the modeling–methodological development of the application of mathematical systems theory in population biology. A discrete-time nonlinear Leslie-type model is considered, where both the reproduction and survival rates decrease as the total population size increases. In this context, the monitoring problem means that, from the observation of the size of certain age classes as a function of time, we want to recover (estimate) the whole state process (i.e., the time-dependent size of the rest of the classes). First, for the linearization approach, conditions for the existence and asymptotic stability of a positive equilibrium are obtained, then the discrete-time observer design method is applied to estimate an unknown state trajectory near the equilibrium, where we could observe a single age class. It is also shown how the observer design can be used to detect an unknown change in the environment that affects the population dynamics. The environmental change is supposed to be generated by additional dynamics (exosystem). Now, the Leslie-type model is extended with this exosystem, and the observer design is applied to this extended system. In this way, an estimation can be obtained for different (constant or periodic) environmental changes as well.

Suggested Citation

  • Inmaculada López & Zoltán Varga & Manuel Gámez & József Garay, 2022. "Monitoring in a Discrete-Time Nonlinear Age-Structured Population Model with Changing Environment," Mathematics, MDPI, vol. 10(15), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2707-:d:876925
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    References listed on IDEAS

    as
    1. Varga, Z., 1992. "On observability of Fisher's model of selection," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 3(1), pages 15-25.
    2. Alejandro F. Villaverde, 2019. "Observability and Structural Identifiability of Nonlinear Biological Systems," Complexity, Hindawi, vol. 2019, pages 1-12, January.
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