View in EDS

Calculating Basins of Attraction Using CUDA: High-Resolution Mapping of Multistable Dynamics.

Saved in:
Bibliographic Details
Title: Calculating Basins of Attraction Using CUDA: High-Resolution Mapping of Multistable Dynamics.
Authors: Rybin, Vyacheslav1 (AUTHOR) vgrybin@etu.ru, Babkin, Ivan1 (AUTHOR) iababkin@etu.ru, Ostrovskii, Valerii1 (AUTHOR) vyostrovskii@etu.ru, Gerasimov, Artemiy2 (AUTHOR) amgerasimov1@stud.etu.ru, Noskov, Evgenii2 (AUTHOR) esnoskov@stud.etu.ru, Butusov, Denis2 (AUTHOR) dnbutusov@etu.ru
Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Jun2026, Vol. 36 Issue 8, p1-21. 21p.
Subjects: CUDA (Computer architecture), Nonlinear dynamical systems, Clustering algorithms, Parallel programming, Data visualization, Computer simulation
Abstract: Plotting basins of attraction reveals the global behavior of nonlinear dynamical systems, specifically in the case of multistability when multiple attractors coexist for a fixed set of parameters. However, calculation of high-resolution diagrams of attraction basins is computationally demanding due to the need for extensive numerical simulation across a large grid of initial conditions. To address this problem, we present a novel GPU-accelerated framework for efficient and scalable computation of basins of attraction using the CUDA toolkit. Our approach combines parallelized trajectory calculation with a robust feature-based clustering strategy that leverages mean peak amplitudes and mean inter-peak intervals with evaluation of fixed-point, unbound, and oscillatory regimes. In addition, we introduce an augmented data representation preserving full distributions of dynamical features, enabling subsequent analysis and parameter adjustment without additional simulation. The proposed method is validated across a diverse set of multistable systems, including cases of finite multistability, megastability, Matryoshka multistability, and extreme multistability. All designed software and obtained data have been published in public repositories to support reproducibility of the study. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 193401824
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Calculating Basins of Attraction Using CUDA: High-Resolution Mapping of Multistable Dynamics.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Rybin%2C+Vyacheslav%22">Rybin, Vyacheslav</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> vgrybin@etu.ru</i><br /><searchLink fieldCode="AR" term="%22Babkin%2C+Ivan%22">Babkin, Ivan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> iababkin@etu.ru</i><br /><searchLink fieldCode="AR" term="%22Ostrovskii%2C+Valerii%22">Ostrovskii, Valerii</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> vyostrovskii@etu.ru</i><br /><searchLink fieldCode="AR" term="%22Gerasimov%2C+Artemiy%22">Gerasimov, Artemiy</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> amgerasimov1@stud.etu.ru</i><br /><searchLink fieldCode="AR" term="%22Noskov%2C+Evgenii%22">Noskov, Evgenii</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> esnoskov@stud.etu.ru</i><br /><searchLink fieldCode="AR" term="%22Butusov%2C+Denis%22">Butusov, Denis</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> dnbutusov@etu.ru</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Bifurcation+%26+Chaos+in+Applied+Sciences+%26+Engineering%22">International Journal of Bifurcation & Chaos in Applied Sciences & Engineering</searchLink>. Jun2026, Vol. 36 Issue 8, p1-21. 21p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22CUDA+%28Computer+architecture%29%22">CUDA (Computer architecture)</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+dynamical+systems%22">Nonlinear dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Clustering+algorithms%22">Clustering algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Parallel+programming%22">Parallel programming</searchLink><br /><searchLink fieldCode="DE" term="%22Data+visualization%22">Data visualization</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Plotting basins of attraction reveals the global behavior of nonlinear dynamical systems, specifically in the case of multistability when multiple attractors coexist for a fixed set of parameters. However, calculation of high-resolution diagrams of attraction basins is computationally demanding due to the need for extensive numerical simulation across a large grid of initial conditions. To address this problem, we present a novel GPU-accelerated framework for efficient and scalable computation of basins of attraction using the CUDA toolkit. Our approach combines parallelized trajectory calculation with a robust feature-based clustering strategy that leverages mean peak amplitudes and mean inter-peak intervals with evaluation of fixed-point, unbound, and oscillatory regimes. In addition, we introduce an augmented data representation preserving full distributions of dynamical features, enabling subsequent analysis and parameter adjustment without additional simulation. The proposed method is validated across a diverse set of multistable systems, including cases of finite multistability, megastability, Matryoshka multistability, and extreme multistability. All designed software and obtained data have been published in public repositories to support reproducibility of the study. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=193401824
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1142/S021812742630017X
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 21
        StartPage: 1
    Subjects:
      – SubjectFull: CUDA (Computer architecture)
        Type: general
      – SubjectFull: Nonlinear dynamical systems
        Type: general
      – SubjectFull: Clustering algorithms
        Type: general
      – SubjectFull: Parallel programming
        Type: general
      – SubjectFull: Data visualization
        Type: general
      – SubjectFull: Computer simulation
        Type: general
    Titles:
      – TitleFull: Calculating Basins of Attraction Using CUDA: High-Resolution Mapping of Multistable Dynamics.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Rybin, Vyacheslav
      – PersonEntity:
          Name:
            NameFull: Babkin, Ivan
      – PersonEntity:
          Name:
            NameFull: Ostrovskii, Valerii
      – PersonEntity:
          Name:
            NameFull: Gerasimov, Artemiy
      – PersonEntity:
          Name:
            NameFull: Noskov, Evgenii
      – PersonEntity:
          Name:
            NameFull: Butusov, Denis
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 30
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 02181274
          Numbering:
            – Type: volume
              Value: 36
            – Type: issue
              Value: 8
          Titles:
            – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
              Type: main
ResultId 1