title: Permanence Analysis for Continuous and Discrete-time Generalized Lotka-Volterra Models with Delay and Switching of Parameters
metadata.name: dc.contributor.author
metadata.value: Aleksandrov, Alexander Yur'evich
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-12-02T15:56:05Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-12-02T15:56:05Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-09
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu35.2024.302
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/48055
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper is addressed to the permanence problem for a generalized Lotka-Volterra system modeling interaction of species in a biological community. The impact of a constant delay and switching of parameters on the dynamics of the system is taken into account. Our analysis is based on the Lyapunov direct method. An original construction of a Lyapunov--Krasovskii functional is proposed. The conditions for the existence of such a functional are formulated in terms of feasibility of special systems of linear algebraic inequalities. It is proved that, under these conditions, the investigated system is permanent for any constant positive delay and any admissible switching signal. In addition, a discrete-time counterpart of the considered model is studied for which the permanence analysis is fulfilled, as well. A comparison of the obtained permanence conditions with known ones is provided. It is shown that the constraints on the system parameters derived in this paper are less conservative.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
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: Differential Equations and Control Processes;Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: population dynamics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: ultimate boundedness
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: permanence
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: delay
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: switching
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov–Krasovskii functional
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Permanence Analysis for Continuous and Discrete-time Generalized Lotka-Volterra Models with Delay and Switching of Parameters
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 24302-jdecp-alexandrov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/48055/1/24302-jdecp-alexandrov.pdf
resources.format: Adobe PDF
resources.size: 128,46 kB