3,767 research outputs found
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
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
Topological data analysis of contagion maps for examining spreading processes on networks
Social and biological contagions are influenced by the spatial embeddedness
of networks. Historically, many epidemics spread as a wave across part of the
Earth's surface; however, in modern contagions long-range edges -- for example,
due to airline transportation or communication media -- allow clusters of a
contagion to appear in distant locations. Here we study the spread of
contagions on networks through a methodology grounded in topological data
analysis and nonlinear dimension reduction. We construct "contagion maps" that
use multiple contagions on a network to map the nodes as a point cloud. By
analyzing the topology, geometry, and dimensionality of manifold structure in
such point clouds, we reveal insights to aid in the modeling, forecast, and
control of spreading processes. Our approach highlights contagion maps also as
a viable tool for inferring low-dimensional structure in networks.Comment: Main Text and Supplementary Informatio
Efficient Algorithms for Distributed Detection of Holes and Boundaries in Wireless Networks
We propose two novel algorithms for distributed and location-free boundary
recognition in wireless sensor networks. Both approaches enable a node to
decide autonomously whether it is a boundary node, based solely on connectivity
information of a small neighborhood. This makes our algorithms highly
applicable for dynamic networks where nodes can move or become inoperative.
We compare our algorithms qualitatively and quantitatively with several
previous approaches. In extensive simulations, we consider various models and
scenarios. Although our algorithms use less information than most other
approaches, they produce significantly better results. They are very robust
against variations in node degree and do not rely on simplified assumptions of
the communication model. Moreover, they are much easier to implement on real
sensor nodes than most existing approaches.Comment: extended version of accepted submission to SEA 201
Topological properties and fractal analysis of recurrence network constructed from fractional Brownian motions
Many studies have shown that we can gain additional information on time
series by investigating their accompanying complex networks. In this work, we
investigate the fundamental topological and fractal properties of recurrence
networks constructed from fractional Brownian motions (FBMs). First, our
results indicate that the constructed recurrence networks have exponential
degree distributions; the relationship between and of recurrence networks decreases with the Hurst
index of the associated FBMs, and their dependence approximately satisfies
the linear formula . Moreover, our numerical results of
multifractal analysis show that the multifractality exists in these recurrence
networks, and the multifractality of these networks becomes stronger at first
and then weaker when the Hurst index of the associated time series becomes
larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst
index possess the strongest multifractality. In addition, the
dependence relationships of the average information dimension on the Hurst index can also be
fitted well with linear functions. Our results strongly suggest that the
recurrence network inherits the basic characteristic and the fractal nature of
the associated FBM series.Comment: 25 pages, 1 table, 15 figures. accepted by Phys. Rev.
Nonlinear time-series analysis revisited
In 1980 and 1981, two pioneering papers laid the foundation for what became
known as nonlinear time-series analysis: the analysis of observed
data---typically univariate---via dynamical systems theory. Based on the
concept of state-space reconstruction, this set of methods allows us to compute
characteristic quantities such as Lyapunov exponents and fractal dimensions, to
predict the future course of the time series, and even to reconstruct the
equations of motion in some cases. In practice, however, there are a number of
issues that restrict the power of this approach: whether the signal accurately
and thoroughly samples the dynamics, for instance, and whether it contains
noise. Moreover, the numerical algorithms that we use to instantiate these
ideas are not perfect; they involve approximations, scale parameters, and
finite-precision arithmetic, among other things. Even so, nonlinear time-series
analysis has been used to great advantage on thousands of real and synthetic
data sets from a wide variety of systems ranging from roulette wheels to lasers
to the human heart. Even in cases where the data do not meet the mathematical
or algorithmic requirements to assure full topological conjugacy, the results
of nonlinear time-series analysis can be helpful in understanding,
characterizing, and predicting dynamical systems
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