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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.
Analyzing data from paleoclimate archives such as tree rings or lake sediments offers the opportunity of inferring information on past climate variability. Often, such data sets are univariate and a proper reconstruction of the systems higher-dimensi
The process of collecting and organizing sets of observations represents a common theme throughout the history of science. However, despite the ubiquity of scientists measuring, recording, and analyzing the dynamics of different processes, an extensi
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling relation over
An effective modeling method for nonlinear distributed parameter systems (DPSs) is critical for both physical system analysis and industrial engineering. In this Rapid Communication, we propose a novel DPS modeling approach, in which a high-order non
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based mul