76 research outputs found
Small-world behavior in a system of mobile elements
We analyze the propagation of activity in a system of mobile automata. A
number r L^d of elements move as random walkers on a lattice of dimension d,
while with a small probability p they can jump to any empty site in the system.
We show that this system behaves as a Dynamic Small-World (DSW) and present
analytic and numerical results for several quantities. Our analysis shows that
the persistence time T* (equivalent to the persistence size L* of small-world
networks) scales as T* ~ (r p)^(-t), with t = 1/(d+1).Comment: To appear in Europhysics Letter
Quasiperiodic graphs at the onset of chaos
We examine the connectivity fluctuations across networks obtained when the
horizontal visibility (HV) algorithm is used on trajectories generated by
nonlinear circle maps at the quasiperiodic transition to chaos. The resultant
HV graph is highly anomalous as the degrees fluctuate at all scales with
amplitude that increases with the size of the network. We determine families of
Pesin-like identities between entropy growth rates and generalized
graph-theoretical Lyapunov exponents. An irrational winding number with pure
periodic continued fraction characterizes each family. We illustrate our
results for the so-called golden, silver and bronze numbers.Comment: arXiv admin note: text overlap with arXiv:1205.190
From time series to complex networks: the visibility graph
In this work we present a simple and fast computational method, the
visibility algorithm, that converts a time series into a graph. The constructed
graph inherits several properties of the series in its structure. Thereby,
periodic series convert into regular graphs, and random series do so into
random graphs. Moreover, fractal series convert into scale-free networks,
enhancing the fact that power law degree distributions are related to
fractality, something highly discussed recently. Some remarkable examples and
analytical tools are outlined in order to test the method's reliability. Many
different measures, recently developed in the complex network theory, could by
means of this new approach characterize time series from a new point of view
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