title: Convergence conditions for continuous and discrete models of population dynamics
metadata.name: dc.contributor.author
metadata.value: Aleksandrov, Alexander Yu.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-03-14T13:07:08Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-03-14T13:07:08Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Aleksandrov, A. Y. (2023). Convergence conditions for continuous and discrete models of population dynamics. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 18(4), 443-453.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2022.401
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/39304
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Some classes of continuous and discrete generalized Volterra models of population dynamics are considered. It is supposed that there are relationships of the type "symbiosis", "compensationism" or "neutralism" between any two species in a biological community. The objective of the work is to obtain conditions under which the investigated models possess the convergence property. This means that the studying system admits a bounded solution that is globally asimptotically stable. To determine the required conditions, the V. I. Zubov's approach and its discrete-time counterpart are used. Constructions of Lyapunov functions are proposed, and with the aid of these functions, the convergence problem for the considered models is reduced to the problem of the existence of positive solutions for some systems of linear algebraic inequalities. In the case where parameters of models are almost periodic functions, the fulfilment of the derived conditions implies that limiting bounded solutions are almost periodic, as well. An example is presented illustrating the obtained theoretical conclusions.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 18; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: population dynamics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: convergence
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: almost
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: periodic oscillations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov functions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Convergence conditions for continuous and discrete models of population dynamics
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 15433-Текст статьи-51653-1-10-20230226.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/39304/1/15433-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-51653-1-10-20230226.pdf
resources.format: Adobe PDF
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