8,502 research outputs found
Detecting Topology Variations in Dynamical Networks
This paper considers the problem of detecting topology variations in
dynamical networks. We consider a network whose behavior can be represented via
a linear dynamical system. The problem of interest is then that of finding
conditions under which it is possible to detect node or link disconnections
from prior knowledge of the nominal network behavior and on-line measurements.
The considered approach makes use of analysis tools from switching systems
theory. A number of results are presented along with examples
Derivative-variable correlation reveals the structure of dynamical networks
We propose a conceptually novel method of reconstructing the topology of
dynamical networks. By examining the correlation between the variable of one
node and the derivative of another node, we derive a simple matrix equation
yielding the network adjacency matrix. Our assumptions are the possession of
time series describing the network dynamics, and the precise knowledge of the
interaction functions. Our method involves a tunable parameter, allowing for
the reconstruction precision to be optimized within the constraints of given
dynamical data. The method is illustrated on a simple example, and the
dependence of the reconstruction precision on the dynamical properties of time
series is discussed. Our theory is in principle applicable to any weighted or
directed network whose internal interaction functions are known.Comment: Submitted to EPJ
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
Quantifying sudden changes in dynamical systems using symbolic networks
We characterise the evolution of a dynamical system by combining two
well-known complex systems' tools, namely, symbolic ordinal analysis and
networks. From the ordinal representation of a time-series we construct a
network in which every node weights represents the probability of an ordinal
patterns (OPs) to appear in the symbolic sequence and each edges weight
represents the probability of transitions between two consecutive OPs. Several
network-based diagnostics are then proposed to characterize the dynamics of
different systems: logistic, tent and circle maps. We show that these
diagnostics are able to capture changes produced in the dynamics as a control
parameter is varied. We also apply our new measures to empirical data from
semiconductor lasers and show that they are able to anticipate the polarization
switchings, thus providing early warning signals of abrupt transitions.Comment: 18 pages, 9 figures, to appear in New Journal of Physic
Graph Theory and Networks in Biology
In this paper, we present a survey of the use of graph theoretical techniques
in Biology. In particular, we discuss recent work on identifying and modelling
the structure of bio-molecular networks, as well as the application of
centrality measures to interaction networks and research on the hierarchical
structure of such networks and network motifs. Work on the link between
structural network properties and dynamics is also described, with emphasis on
synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape
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