title: On the diagonal stability of some classes of complex systems
metadata.name: dc.contributor.author
metadata.value: Aleksandrov, Alexander Yu.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Vorob’eva, Anna A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kolpak, Eugeny P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-07-18T11:48:59Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-07-18T11:48:59Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Aleksandrov A. Yu., Vorob’eva A. A., Kolpak E. P. On the diagonal stability of some classes of complex systems. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2018, vol. 14, iss. 2, pp. 72–88.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11702/spbu10.2018.201
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/10439
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper deals with the problem of diagonal stability of nonlinear difference-differential
  systems. Certain classes of complex systems with delay and nonlinearities of a sector type
  are studied. It is assumed that these systems describe the interaction of two-dimensional
  blockswith a delay in connections between the blocks. Two kinds of structure of connections
  are investigated. For every kind, necessary and sufficient conditions for the existence of
  diagonal Lyapunov—Krasovskii functionals are found. The existence of such functionals
  guarantees the asymptotic stability of the zero solutions of considered systems for any
  nonnegative delay and any admissible nonlinearities. These conditions are formulated in
  terms of the Hurwitz property of specially constructed Metzler matrices. The proposed
  approaches are used for the stability analysis ofsome models of population dynamics.
  Generalized Lotka—Volterra models composed of several interacting pairs of predator-prey
  type are investigated. With the aid of the Lyapunov direct method and diagonal Lyapunov—
  Krasovskii functionals, conditions are derived under which equilibrium positions of the
  considered models are globally asymptotically stable in the positive orthant of the state space
  for any nonnegative delay. An illustrative example and results of the numerical simulation
  are presented to demonstrate the effectiveness of the developed approaches.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при частичной финансовой поддержке Российского фонда фундаментальных исследований (грант № 16-01-00587-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 14; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: diagonal stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: complex system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: delay
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: population dynamics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov—Krasovskii functional
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the diagonal stability of some classes of complex systems
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01-Aleksandrov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/10439/1/01-Aleksandrov.pdf
resources.format: Adobe PDF
resources.size: 362,32 kB