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Minimal cover of high-dimensional chaotic attractors by embedded coherent structures

journal contribution
posted on 2024-10-29, 10:14 authored by DL Crane, Ruslan DavidchackRuslan Davidchack, Alexander GorbanAlexander Gorban
We propose a general method for constructing a minimal cover of high-dimensional chaotic attractors by embedded coherent structures, such as periodic orbits. By minimal cover we mean a finite subset of periodic orbits such that any point on the attractor is within a predefined proximity threshold to a periodic orbit within the subset. The proximity measure can be chosen with considerable freedom and adapted to the properties of a given attractor. On the example of a Kuramoto-Sivashinsky chaotic attractor, we demonstrate that the minimal cover can be faithfully constructed even when the proximity measure is defined within a subspace of dimension much smaller than the dimension of space containing the attractor. We discuss how the minimal cover can be used to provide reduced characterisation of the attractor structure and dynamics on it.

History

Author affiliation

College of Science & Engineering Comp' & Math' Sciences

Version

  • AM (Accepted Manuscript)

Published in

Communications in Nonlinear Science and Numerical Simulation

Volume

140

Issue

1

Pagination

108345

Publisher

Elsevier

issn

1007-5704

eissn

1878-7274

Copyright date

2024

Available date

2025-09-16

Language

en

Deposited by

Professor Ruslan Davidchack

Deposit date

2024-10-22

Data Access Statement

Data will be made available on request.

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