749 research outputs found
Critical behavior of a cellular automaton highway traffic model
We derive the critical behavior of a CA traffic flow model using an order
parameter breaking the symmetry of the jam-free phase. Random braking appears
to be the symmetry-breaking field conjugate to the order parameter. For
, we determine the values of the critical exponents ,
and using an order-3 cluster approximation and computer
simulations. These critical exponents satisfy a scaling relation, which can be
derived assuming that the order parameter is a generalized homogeneous function
of and p in the vicinity of the phase transition point.Comment: 6 pages, 12 figure
Randomized Cellular Automata
We define and study a few properties of a class of random automata networks.
While regular finite one-dimensional cellular automata are defined on periodic
lattices, these automata networks, called randomized cellular automata, are
defined on random directed graphs with constant out-degrees and evolve
according to cellular automaton rules. For some families of rules, a few
typical a priori unexpected results are presented.Comment: 13 pages, 7 figure
Conservation Laws in Cellular Automata
If X is a discrete abelian group and B a finite set, then a cellular
automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts.
If g is a real-valued function on B, then, for any b in B^X, we define G(b) to
be the sum over all x in X of g(b_x) (if finite). We say g is `conserved' by F
if G is constant under the action of F. We characterize such `conservation
laws' in several ways, deriving both theoretical consequences and practical
tests, and provide a method for constructing all one-dimensional CA exhibiting
a given conservation law.Comment: 19 pages, LaTeX 2E with one (1) Encapsulated PostScript figure. To
appear in Nonlinearity. (v2) minor changes/corrections; new references added
to bibliograph
Probabilistic cellular automata with conserved quantities
We demonstrate that the concept of a conservation law can be naturally
extended from deterministic to probabilistic cellular automata (PCA) rules. The
local function for conservative PCA must satisfy conditions analogous to
conservation conditions for deterministic cellular automata. Conservation
condition for PCA can also be written in the form of a current conservation
law. For deterministic nearest-neighbour CA the current can be computed
exactly. Local structure approximation can partially predict the equilibrium
current for non-deterministic cases. For linear segments of the fundamental
diagram it actually produces exact results.Comment: 17 pages, 2 figure
5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal
We study two-dimensional rotation-symmetric number-conserving cellular
automata working on the von Neumann neighborhood (RNCA). It is known that such
automata with 4 states or less are trivial, so we investigate the possible
rules with 5 states. We give a full characterization of these automata and show
that they cannot be strongly Turing universal. However, we give example of
constructions that allow to embed some boolean circuit elements in a 5-states
RNCA
Max-plus analysis on some binary particle systems
We concern with a special class of binary cellular automata, i.e., the
so-called particle cellular automata (PCA) in the present paper. We first
propose max-plus expressions to PCA of 4 neighbors. Then, by utilizing basic
operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2
and 4-3 are solved exactly and their general solutions are found in terms of
max-plus expressions. Finally, we analyze the asymptotic behaviors of general
solutions and prove the fundamental diagrams exactly.Comment: 24 pages, 5 figures, submitted to J. Phys.
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
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