Blog
About

17
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Predicting the bounds of large chaotic systems using low-dimensional manifolds

      *

      PLoS ONE

      Public Library of Science

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          Predicting extrema of chaotic systems in high-dimensional phase space remains a challenge. Methods, which give extrema that are valid in the long term, have thus far been restricted to models of only a few variables. Here, a method is presented which treats extrema of chaotic systems as belonging to discretised manifolds of low dimension (low-D) embedded in high-dimensional (high-D) phase space. As a central feature, the method exploits that strange attractor dimension is generally much smaller than parent system phase space dimension. This is important, since the computational cost associated with discretised manifolds depends exponentially on their dimension. Thus, systems that would otherwise be associated with tremendous computational challenges, can be tackled on a laptop. As a test, bounding manifolds are calculated for high-D modifications of the canonical Duffing system. Parameters can be set such that the bounding manifold displays harmonic behaviour even if the underlying system is chaotic. Thus, solving for one post-transient forcing cycle of the bounding manifold predicts the extrema of the underlying chaotic problem indefinitely.

          Related collections

          Most cited references 48

          • Record: found
          • Abstract: not found
          • Article: not found

          Geometry from a Time Series

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            An equation for continuous chaos

             O.E. Rössler (1976)
              Bookmark
              • Record: found
              • Abstract: not found
              • Book Chapter: not found

              Detecting strange attractors in turbulence

               Floris Takens (1981)
                Bookmark

                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                2017
                23 June 2017
                : 12
                : 6
                Affiliations
                University of Oxford, Medical sciences division, Oxford, OX3 9DU, United Kingdom
                Tongji University, CHINA
                Author notes

                Competing Interests: The author has declared that no competing interests exist.

                • Conceptualization: AMH.

                • Data curation: AMH.

                • Formal analysis: AMH.

                • Funding acquisition: AMH.

                • Investigation: AMH.

                • Methodology: AMH.

                • Project administration: AMH.

                • Resources: AMH.

                • Software: AMH.

                • Supervision: AMH.

                • Validation: AMH.

                • Visualization: AMH.

                • Writing – original draft: AMH.

                • Writing – review & editing: AMH.

                [¤]

                Current address: King’s College Hospital, Weston Education Centre, 1st Floor, Denmark Hill, London SE5 9RS, United Kingdom

                Article
                PONE-D-16-47871
                10.1371/journal.pone.0179507
                5482462
                28644871
                © 2017 Asger M. Haugaard

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                Page count
                Figures: 12, Tables: 1, Pages: 27
                Product
                Funding
                The work was unfunded and completed by the author in their own time. There were no expenses beyond the time invested.
                Categories
                Research Article
                Physical Sciences
                Mathematics
                Algebra
                Linear Algebra
                Eigenvalues
                Physical Sciences
                Mathematics
                Topology
                Manifolds
                Physical Sciences
                Mathematics
                Geometry
                Tangents
                Computer and Information Sciences
                Systems Science
                Chaotic Systems
                Physical Sciences
                Mathematics
                Systems Science
                Chaotic Systems
                Physical Sciences
                Mathematics
                Algebra
                Linear Algebra
                Vector Spaces
                Physical Sciences
                Mathematics
                Algebra
                Linear Algebra
                Eigenvectors
                Computer and Information Sciences
                Systems Science
                Nonlinear Systems
                Physical Sciences
                Mathematics
                Systems Science
                Nonlinear Systems
                Physical Sciences
                Mathematics
                Applied Mathematics
                Finite Element Analysis
                Custom metadata
                All relevant data are within the paper and its Supporting Information files.

                Uncategorized

                Comments

                Comment on this article