title: Stability of homogeneous nonstationary systems of differential-difference equations with linearly time delay
metadata.name: dc.contributor.author
metadata.value: Ekimov, Alexander V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Chizhova, Olga N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Zaranik, Uliana P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-03-05T11:30:40Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-03-05T11:30:40Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ekimov A. V., Chigova O. N., Zaranik U. P. Stability of homogeneous nonstationary systems of differential-difference equations with linearly time delay. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 4, pp. 415–424.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2019.401
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17154
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: These systems can be considered as a model for the spread of the epidemic in the population.
  In addition, systems with linearly increasing delay describe the dynamics of the information
  server, mixing tank, the process of formation of traffic jams on the ring road, etc. For the
  study, the concept of an average system is introduced. This approach allows us to reduce the
  analysis of the Lyapunov stability problem of the zero solution of the original system to the
  investigation of the zero solution of the averaged system. Sufficient conditions for stationary
  system stability are formulated. Then the application of Razumihin’s approach to the study
  of stability original system is used. The Lyapunov function is constructed. As a result,
  new sufficient conditions for the asymptotic stability of the zero solution of nonstationary
  homogeneous systems with a linearly increasing time delay are obtained. These conditions
  are the generalization of well-known results for the linear systems with a linearly increasing
  time delay.
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 15; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: homogeneous differential-difference system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: linearly increasing time delay
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic stability
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stability of homogeneous nonstationary systems of differential-difference equations with linearly time delay
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 415-424.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17154/1/415-424.pdf
resources.format: Adobe PDF
resources.size: 296,89 kB