Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: State space reconstruction of spatially extended systems and of time
  delayed systems from the time series of a scalar variable   The space-time representation of high-dimensional dynamical systems that have
a well defined characteristic time scale has proven to be very useful to deepen
the understanding of such systems and to uncover hidden features in their
output signals. Genuine analogies between one-dimensional (1D) spatially
extended systems (1D SESs) and time delayed systems (TDSs) have been observed,
including similar pattern formation and propagation of localized structures. An
open question is if such analogies are limited to the space-time
representation, or, if it is possible to reconstruct similar attractors, from
the time series of an observed variable. In this work we address this issue by
considering a bistable 1D SES and two TDSs (a bistable system and a model of
two lasers with time delayed coupling). In these three examples we find that we
can reconstruct the underlying attractor in a three-dimensional pseudo-space,
where the evolution is governed by a polynomial potential. We also discuss the
limitations of the analogy between 1D SESs and TDSs.

0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs