1,990 research outputs found
Measurement of surface roughness slope
Instrument, consisting of isolator, differentiator, absolute value circuit, and integrator, uses output signal from surface texture analyzer profile-amplifier to calculate surface roughness slope. Calculations provide accurate, instantaneous value of the slope. Instrument is inexpensive and applicable to any commerical surface texture analyzer
Geometric signature of complex synchronisation scenarios
Synchronisation between coupled oscillatory systems is a common phenomenon in
many natural as well as technical systems. Varying the strength of coupling
often leads to qualitative changes in the complex dynamics of the mutually
coupled systems including different types of synchronisation such as phase,
lag, generalised, or even complete synchronisation. Here, we study the
geometric signatures of coupling along with the onset of generalised
synchronisation between two coupled chaotic oscillators by mapping the systems'
individual as well as joint recurrences in phase space to a complex network.
For a paradigmatic continuous-time model system, the transitivity properties of
the resulting joint recurrence networks display distinct variations associated
with changes in the structural similarity between different parts of the
considered trajectories. They therefore provide a useful indicator for the
emergence of generalised synchronisation.
This paper is dedicated to the 25th anniversary of the introduction of
recurrence plots by Eckmann et al. (Europhys. Lett. 4 (1987), 973).Comment: 7 pages, 3 figure
Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes
ACKNOWLEDGMENTS MW and RVD have been supported by the German Federal Ministry for Education and Research (BMBF) via the Young Investigators Group CoSy-CC2 (grant no. 01LN1306A). JFD thanks the Stordalen Foundation and BMBF (project GLUES) for financial support. JK acknowledges the IRTG 1740 funded by DFG and FAPESP. MT Gastner is acknowledged for providing his data on the airline, interstate, and Internet network. P Menck thankfully provided his data on the Scandinavian power grid. We thank S Willner on behalf of the entire zeean team for providing the data on the world trade network. All computations have been performed using the Python package pyunicorn [41] that is available at https://github.com/pik-copan/pyunicorn.Peer reviewedPreprin
Recurrence networks - A novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing structural properties of
time series from complex systems. Starting from the concept of recurrences in
phase space, the recurrence matrix of a time series is interpreted as the
adjacency matrix of an associated complex network which links different points
in time if the evolution of the considered states is very similar. A critical
comparison of these recurrence networks with similar existing techniques is
presented, revealing strong conceptual benefits of the new approach which can
be considered as a unifying framework for transforming time series into complex
networks that also includes other methods as special cases.
It is demonstrated that there are fundamental relationships between the
topological properties of recurrence networks and the statistical properties of
the phase space density of the underlying dynamical system. Hence, the network
description yields new quantitative characteristics of the dynamical complexity
of a time series, which substantially complement existing measures of
recurrence quantification analysis
Disentangling different types of El Ni\~no episodes by evolving climate network analysis
Complex network theory provides a powerful toolbox for studying the structure
of statistical interrelationships between multiple time series in various
scientific disciplines. In this work, we apply the recently proposed climate
network approach for characterizing the evolving correlation structure of the
Earth's climate system based on reanalysis data of surface air temperatures. We
provide a detailed study on the temporal variability of several global climate
network characteristics. Based on a simple conceptual view on red climate
networks (i.e., networks with a comparably low number of edges), we give a
thorough interpretation of our evolving climate network characteristics, which
allows a functional discrimination between recently recognized different types
of El Ni\~no episodes. Our analysis provides deep insights into the Earth's
climate system, particularly its global response to strong volcanic eruptions
and large-scale impacts of different phases of the El Ni\~no Southern
Oscillation (ENSO).Comment: 20 pages, 12 figure
Quasiperiodic graphs: structural design, scaling and entropic properties
A novel class of graphs, here named quasiperiodic, are constructed via
application of the Horizontal Visibility algorithm to the time series generated
along the quasiperiodic route to chaos. We show how the hierarchy of
mode-locked regions represented by the Farey tree is inherited by their
associated graphs. We are able to establish, via Renormalization Group (RG)
theory, the architecture of the quasiperiodic graphs produced by irrational
winding numbers with pure periodic continued fraction. And finally, we
demonstrate that the RG fixed-point degree distributions are recovered via
optimization of a suitably defined graph entropy
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