title: Permanence conditions for models of population dynamics with switches and delay
metadata.name: dc.contributor.author
metadata.value: Aleksandrov, Alexander Yu.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-08-24T19:17:40Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-08-24T19:17:40Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Aleksandrov A. Yu. Permanence conditions for models of population dynamics with switches and delay. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2020, vol. 16, iss. 2, pp. 88–99.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2020.201
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/19011
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Some classes of discrete and continuous generalized Volterra models of population dynamics
  with parameter switching and constant delay are studied. It is assumed that there are
  relationships of the type “symbiosis”, “compensationism” or “neutralism” between any two
  species in a biological community. The goal of the work is to obtain sufficient conditions for the permanence of such models. Original constructions of common Lyapunov—Krasovsky
  functionals are proposed for families of subsystems corresponding to the switched systems
  under consideration. Using the constructed functionals, conditions are derived that guarantee
  permanence for any admissible switching laws and any constant nonnegative delay. These
  conditions are constructive and are formulated in terms of the existence of a positive solution
  for an auxiliary system of linear algebraic inequalities. It should be noted that, in the
  proved theorems, the persistence of the systems is ensured by the positive coefficients of
  natural growth and the beneficial effect of populations on each other, whereas the ultimate
  boundedness of species numbers is provided by the intraspecific competition. An example is
  presented demonstrating the effectiveness of the developed approaches.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by the Russian Foundation for Basic Research (grant N 19-01-00146-a).
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 16; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: population dynamics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: permanence
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: ultimate boundedness
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: switches
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: delay
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov— Krasovskii functional
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Permanence conditions for models of population dynamics with switches and delay
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 88-99.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/19011/1/88-99.pdf
resources.format: Adobe PDF
resources.size: 275,86 kB