title: On the conditions for cycles existence in a second-order discrete-time system with sector-nonlinearity
metadata.name: dc.contributor.author
metadata.value: Zvyagintseva, Tatiana E.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-05-04T19:13:55Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-05-04T19:13:55Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zvyagintseva Т.Е. On the conditions for cycles existence in a second-order discrete-time system with sector-nonlinearity. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 1, pp. 63–72.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.106
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/28434
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper, a second-order discrete-time automatic control system is studied. This work is
  a continuation of the research presented in the author’s papers “On the Aizerman problem:
  coefficient conditions for the existence of a four-period cycle in a second-order discrete-time
  system” and “On the Aizerman problem: coefficient conditions for the existence of threeand
  six-period cycles in a second-order discrete-time system”, where systems with two- and
  three-periodic nonlinearities lying in the Hurwitz angle were considered. The systems with
  nonlinearities subjected to stronger constraints are discussed in this paper. It is assumed
  that the nonlinearity not only lies in the Hurwitz angle, but also satisfies the additional
  sector-condition. This formulation of the problem is found in many works devoted to theoretical
  and applied questions of the automatic control theory. In this paper, a system with
  such nonlinearity is explored for all possible values of the parameters. It is shown that in
  this case there are parameter values for which a system with a two-periodic nonlinearity
  has a family of four-period cycles, and a system with a three-periodic nonlinearity has a
  family of three- or six-period cycles. The conditions on the parameters under which the
  system can have a family of periodic solutions are written out explicitly. The proofs of the
  theorems provide a method for constructing nonlinearity in such a way that any solution
  of the system with initial data lying on some definite ray is periodic.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported in part by Russian Foundation for Basic Research (grant no. 19-01-00388).
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. Mathematics. Mechanics. Astronomy;Volume 8 (66); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: second-order discrete-time system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Aizerman conjecture
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: sector nonlinearity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: absolute stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: periodic solution
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the conditions for cycles existence in a second-order discrete-time system with sector-nonlinearity
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 63-72.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/28434/1/63-72.pdf
resources.format: Adobe PDF
resources.size: 656,19 kB