2,014 research outputs found
Control of cellular automata
We study the problem of master-slave synchronization and control of
totalistic cellular automata (CA) by putting a fraction of sites of the slave
equal to those of the master and finding the distance between both as a
function of this fraction. We present three control strategies that exploit
local information about the CA, mainly, the number of nonzero Boolean
derivatives. When no local information is used, we speak of synchronization. We
find the critical properties of control and discuss the best control strategy
compared with synchronization
Second-Order Dynamics in the Collective Evolution of Coupled Maps and Automata
We review recent numerical studies and the phenomenology of spatially
synchronized collective states in many-body dynamical systems. These states
exhibit thermodynamic noise superimposed on the collective, quasiperiodic order
parameter evolution with typically one basic irrational frequency. We
concentrate on the description of the global temporal properties in terms of
second-order difference equations.Comment: 11 pages (plain TeX), 4 figures (PostScript), preprint OUTP-92-51
Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models
Spatially explicit models have been widely used in today's mathematical
ecology and epidemiology to study persistence and extinction of populations as
well as their spatial patterns. Here we extend the earlier work--static
dispersal between neighbouring individuals to mobility of individuals as well
as multi-patches environment. As is commonly found, the basic reproductive
ratio is maximized for the evolutionary stable strategy (ESS) on diseases'
persistence in mean-field theory. This has important implications, as it
implies that for a wide range of parameters that infection rate will tend
maximum. This is opposite with present results obtained in spatial explicit
models that infection rate is limited by upper bound. We observe the emergence
of trade-offs of extinction and persistence on the parameters of the infection
period and infection rate and show the extinction time having a linear
relationship with respect to system size. We further find that the higher
mobility can pronouncedly promote the persistence of spread of epidemics, i.e.,
the phase transition occurs from extinction domain to persistence domain, and
the spirals' wavelength increases as the mobility increasing and ultimately, it
will saturate at a certain value. Furthermore, for multi-patches case, we find
that the lower coupling strength leads to anti-phase oscillation of infected
fraction, while higher coupling strength corresponds to in-phase oscillation.Comment: 12page
Identification of cellular automata based on incomplete observations with bounded time gaps
In this paper, the problem of identifying the cellular automata (CAs) is considered. We frame and solve this problem in the context of incomplete observations, i.e., prerecorded, incomplete configurations of the system at certain, and unknown time stamps. We consider 1-D, deterministic, two-state CAs only. An identification method based on a genetic algorithm with individuals of variable length is proposed. The experimental results show that the proposed method is highly effective. In addition, connections between the dynamical properties of CAs (Lyapunov exponents and behavioral classes) and the performance of the identification algorithm are established and analyzed
A way to synchronize models with seismic faults for earthquake forecasting: Insights from a simple stochastic model
Numerical models are starting to be used for determining the future behaviour
of seismic faults and fault networks. Their final goal would be to forecast
future large earthquakes. In order to use them for this task, it is necessary
to synchronize each model with the current status of the actual fault or fault
network it simulates (just as, for example, meteorologists synchronize their
models with the atmosphere by incorporating current atmospheric data in them).
However, lithospheric dynamics is largely unobservable: important parameters
cannot (or can rarely) be measured in Nature. Earthquakes, though, provide
indirect but measurable clues of the stress and strain status in the
lithosphere, which should be helpful for the synchronization of the models. The
rupture area is one of the measurable parameters of earthquakes. Here we
explore how it can be used to at least synchronize fault models between
themselves and forecast synthetic earthquakes. Our purpose here is to forecast
synthetic earthquakes in a simple but stochastic (random) fault model. By
imposing the rupture area of the synthetic earthquakes of this model on other
models, the latter become partially synchronized with the first one. We use
these partially synchronized models to successfully forecast most of the
largest earthquakes generated by the first model. This forecasting strategy
outperforms others that only take into account the earthquake series. Our
results suggest that probably a good way to synchronize more detailed models
with real faults is to force them to reproduce the sequence of previous
earthquake ruptures on the faults. This hypothesis could be tested in the
future with more detailed models and actual seismic data.Comment: Revised version. Recommended for publication in Tectonophysic
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