title: On bifurcations of chaotic attractors in a pulse width modulated control system
metadata.name: dc.contributor.author
metadata.value: Zhusubaliyev, Zhanybai T.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Sopuev, Ulanbek A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Bushuev, Dmitry A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kucherov, Andrey S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Abdirasulov, Aitibek Z.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-04-22T20:32:25Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-04-22T20:32:25Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zhusubaliyev Zh. T., Sopuev U. A., Bushuev D. A., Kucherov A. S., Abdirasulov A. Z. On bifurcations of chaotic attractors in a pulse width modulated control system. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2024, vol. 20, iss. 1, pp. 62–78. https://doi.org/10.21638/11701/spbu10.2024.106 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2024.106
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/45330
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This paper discusses bifurcational phenomena in a control system with pulse-width modulation
  of the first kind. We show that the transition from a regular dynamics to chaos occurs
  in a sequence of classical supercritical period doubling and border collision bifurcations. As
  a parameter is varied, one can observe a cascade of doubling of the cyclic chaotic intervals,
  which are associated with homoclinic bifurcations of unstable periodic orbits. Such transition
  are also refereed as merging bifurcation (known also as merging crisis). At the bifurcation
  point, the unstable periodic orbit collides with some of the boundaries of a chaotic attractor
  and as a result, the periodic orbit becomes a homoclinic. This condition we use for obtain
  equations for bifurcation boundaries in the form of an explicit dependence on the parameters.
  This allow us to determine the regions of stability for periodic orbits and domains of
  the existence of four-, two- and one-band chaotic attractors in the parameter plane.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work of Zh. T. Zhusubaliyev was supported by the Ministry of Education and Science of the
  Russian Federation within the scope of the “Implementation of the Strategic Academic Leadership program
  Priority-2030” (1.73.23 П; 1.7.21/S-2; 1.7.21/4-24-7); U. A. Sopuev and A. Z. Abdirasulov were supported
  by the Osh State University (grants N 14-22; №19-24). The work of D. A. Bushuev was supported within
  the framework of the Program “Priority-2030” using equipment of High Technology Center of the Belgorod
  State Technological University named after V. G. Shukhov.
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 20; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: piecewise smooth bimodal map
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: border collision bifurcations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: homoclinic bifurcations of periodic orbits
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: merging bifurcation of a chaotic attractor
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On bifurcations of chaotic attractors in a pulse width modulated control system
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: vestnik_spbu10_2024_062.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/45330/1/vestnik_spbu10_2024_062.pdf
resources.format: Adobe PDF
resources.size: 4,34 MB