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

Inmaculada López, Zoltán Varga, Manuel Gámez and József Garay
Additional contact information
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

Mathematics, 2022, vol. 10, issue 15, 1-16

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.

Keywords: nonlinear Leslie-type model; observer design; environmental change (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/15/2707/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/15/2707/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:15:p:2707-:d:876925

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().