2,720 research outputs found
Geometric and dynamic perspectives on phase-coherent and noncoherent chaos
Statistically distinguishing between phase-coherent and noncoherent chaotic
dynamics from time series is a contemporary problem in nonlinear sciences. In
this work, we propose different measures based on recurrence properties of
recorded trajectories, which characterize the underlying systems from both
geometric and dynamic viewpoints. The potentials of the individual measures for
discriminating phase-coherent and noncoherent chaotic oscillations are
discussed. A detailed numerical analysis is performed for the chaotic R\"ossler
system, which displays both types of chaos as one control parameter is varied,
and the Mackey-Glass system as an example of a time-delay system with
noncoherent chaos. Our results demonstrate that especially geometric measures
from recurrence network analysis are well suited for tracing transitions
between spiral- and screw-type chaos, a common route from phase-coherent to
noncoherent chaos also found in other nonlinear oscillators. A detailed
explanation of the observed behavior in terms of attractor geometry is given.Comment: 12 pages, 13 figure
Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package
We introduce the \texttt{pyunicorn} (Pythonic unified complex network and
recurrence analysis toolbox) open source software package for applying and
combining modern methods of data analysis and modeling from complex network
theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully
object-oriented and easily parallelizable package written in the language
Python. It allows for the construction of functional networks such as climate
networks in climatology or functional brain networks in neuroscience
representing the structure of statistical interrelationships in large data sets
of time series and, subsequently, investigating this structure using advanced
methods of complex network theory such as measures and models for spatial
networks, networks of interacting networks, node-weighted statistics or network
surrogates. Additionally, \texttt{pyunicorn} provides insights into the
nonlinear dynamics of complex systems as recorded in uni- and multivariate time
series from a non-traditional perspective by means of recurrence quantification
analysis (RQA), recurrence networks, visibility graphs and construction of
surrogate time series. The range of possible applications of the library is
outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure
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
Network Triads: Transitivity, Referral and Venture Capital Decisions in China and Russia
This article examines effects of dyadic ties and interpersonal trust on referrals and investment decisions of venture capitalists in the Chinese and Russian contexts. The study uses the postulate of transitivity of social network theory as a conceptual framework. The findings reveal that referee-venture capitalist tie, referee-entrepreneur tie, and interpersonal trust between referee and venture capitalist have positive effects on referrals and investment decisions of venture capitalists. The institutional, social and cultural differences between China and Russia have minimal effects on referrals. Interpersonal trust has positive effects on investment decisions in Russia.http://deepblue.lib.umich.edu/bitstream/2027.42/40138/3/wp752.pd
On the nature of chaos
Based on newly discovered properties of the shift map (Theorem 1), we believe
that chaos should involve not only nearby points can diverge apart but also
faraway points can get close to each other. Therefore, we propose to call a
continuous map from an infinite compact metric space to itself
chaotic if there exists a positive number such that for any point
and any nonempty open set (not necessarily an open neighborhood of ) in
there is a point in such that and .Comment: 5 page
Densification and Structural Transitions in Networks that Grow by Node Copying
We introduce a growing network model---the copying model---in which a new
node attaches to a randomly selected target node and, in addition,
independently to each of the neighbors of the target with copying probability
. When , this algorithm generates sparse networks, in which
the average node degree is finite. A power-law degree distribution also arises,
with a non-universal exponent whose value is determined by a transcendental
equation in . In the sparse regime, the network is "normal", e.g., the
relative fluctuations in the number of links are asymptotically negligible. For
, the emergent networks are dense (the average degree
increases with the number of nodes ) and they exhibit intriguing structural
behaviors. In particular, the -dependence of the number of -cliques
(complete subgraphs of nodes) undergoes transitions from normal to
progressively more anomalous behavior at a -dependent critical values of
. Different realizations of the network, which start from the same initial
state, exhibit macroscopic fluctuations in the thermodynamic limit---absence of
self averaging. When linking to second neighbors of the target node can occur,
the number of links asymptotically grows as as , so that the
network is effectively complete as .Comment: 15 pages, 12 figure
Recurrence-based time series analysis by means of complex network methods
Complex networks are an important paradigm of modern complex systems sciences
which allows quantitatively assessing the structural properties of systems
composed of different interacting entities. During the last years, intensive
efforts have been spent on applying network-based concepts also for the
analysis of dynamically relevant higher-order statistical properties of time
series. Notably, many corresponding approaches are closely related with the
concept of recurrence in phase space. In this paper, we review recent
methodological advances in time series analysis based on complex networks, with
a special emphasis on methods founded on recurrence plots. The potentials and
limitations of the individual methods are discussed and illustrated for
paradigmatic examples of dynamical systems as well as for real-world time
series. Complex network measures are shown to provide information about
structural features of dynamical systems that are complementary to those
characterized by other methods of time series analysis and, hence,
substantially enrich the knowledge gathered from other existing (linear as well
as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos
(2011
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