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