844 research outputs found
Sublattice synchronization of chaotic networks with delayed couplings
Synchronization of chaotic units coupled by their time delayed variables are
investigated analytically. A new type of cooperative behavior is found:
sublattice synchronization. Although the units of one sublattice are not
directly coupled to each other, they completely synchronize without time delay.
The chaotic trajectories of different sublattices are only weakly correlated
but not related by generalized synchronization. Nevertheless, the trajectory of
one sublattice is predictable from the complete trajectory of the other one.
The spectra of Lyapunov exponents are calculated analytically in the limit of
infinite delay times, and phase diagrams are derived for different topologies
Public Channel Cryptography: Chaos Synchronization and Hilbert's Tenth Problem
The synchronization process of two mutually delayed coupled deterministic
chaotic maps is demonstrated both analytically and numerically. The
synchronization is preserved when the mutually transmitted signal is concealed
by two commutative private filters that are placed on each end of the
communication channel. We demonstrate that when the transmitted signal is a
convolution of the truncated time delayed output signals or some powers of the
delayed output signals synchronization is still maintained. The task of a
passive attacker is mapped onto Hilbert's tenth problem, solving a set of
nonlinear Diophantine equations, which was proven to be in the class of
NP-Complete problems. This bridge between two different disciplines,
synchronization in nonlinear dynamical processes and the realm of the NPC
problems, opens a horizon for a new type of secure public-channel protocols
Transfer-matrix DMRG for stochastic models: The Domany-Kinzel cellular automaton
We apply the transfer-matrix DMRG (TMRG) to a stochastic model, the
Domany-Kinzel cellular automaton, which exhibits a non-equilibrium phase
transition in the directed percolation universality class. Estimates for the
stochastic time evolution, phase boundaries and critical exponents can be
obtained with high precision. This is possible using only modest numerical
effort since the thermodynamic limit can be taken analytically in our approach.
We also point out further advantages of the TMRG over other numerical
approaches, such as classical DMRG or Monte-Carlo simulations.Comment: 9 pages, 9 figures, uses IOP styl
Directed Percolation with a Wall or Edge
We examine the effects of introducing a wall or edge into a directed
percolation process. Scaling ansatzes are presented for the density and
survival probability of a cluster in these geometries, and we make the
connection to surface critical phenomena and field theory. The results of
previous numerical work for a wall can thus be interpreted in terms of surface
exponents satisfying scaling relations generalising those for ordinary directed
percolation. New exponents for edge directed percolation are also introduced.
They are calculated in mean-field theory and measured numerically in 2+1
dimensions.Comment: 14 pages, submitted to J. Phys.
Nature of phase transitions in a probabilistic cellular automaton with two absorbing states
We present a probabilistic cellular automaton with two absorbing states,
which can be considered a natural extension of the Domany-Kinzel model. Despite
its simplicity, it shows a very rich phase diagram, with two second-order and
one first-order transition lines that meet at a tricritical point. We study the
phase transitions and the critical behavior of the model using mean field
approximations, direct numerical simulations and field theory. A closed form
for the dynamics of the kinks between the two absorbing phases near the
tricritical point is obtained, providing an exact correspondence between the
presence of conserved quantities and the symmetry of absorbing states. The
second-order critical curves and the kink critical dynamics are found to be in
the directed percolation and parity conservation universality classes,
respectively. The first order phase transition is put in evidence by examining
the hysteresis cycle. We also study the "chaotic" phase, in which two replicas
evolving with the same noise diverge, using mean field and numerical
techniques. Finally, we show how the shape of the potential of the
field-theoretic formulation of the problem can be obtained by direct numerical
simulations.Comment: 19 pages with 7 figure
Active Width at a Slanted Active Boundary in Directed Percolation
The width W of the active region around an active moving wall in a directed
percolation process diverges at the percolation threshold p_c as W \simeq A
\epsilon^{-\nu_\parallel} \ln(\epsilon_0/\epsilon), with \epsilon=p_c-p,
\epsilon_0 a constant, and \nu_\parallel=1.734 the critical exponent of the
characteristic time needed to reach the stationary state \xi_\parallel \sim
\epsilon^{-\nu_\parallel}. The logarithmic factor arises from screening of
statistically independent needle shaped sub clusters in the active region.
Numerical data confirm this scaling behaviour.Comment: 5 pages, 5 figure
Nonequilibrium Dynamics and Aging in the Three--Dimensional Ising Spin Glass Model
The low temperature dynamics of the three dimensional Ising spin glass in
zero field with a discrete bond distribution is investigated via MC
simulations. The thermoremanent magnetization is found to decay algebraically
and the temperature dependent exponents agree very well with the experimentally
determined values. The nonequilibrium autocorrelation function shows
a crossover at the waiting (or {\em aging}) time from algebraic {\em
quasi-equilibrium} decay for times to another, faster algebraic
decay for with an exponent similar to one for the remanent
magnetization.Comment: Revtex, 11 pages + 4 figures (included as Latex-files
Nonlocal mechanism for cluster synchronization in neural circuits
The interplay between the topology of cortical circuits and synchronized
activity modes in distinct cortical areas is a key enigma in neuroscience. We
present a new nonlocal mechanism governing the periodic activity mode: the
greatest common divisor (GCD) of network loops. For a stimulus to one node, the
network splits into GCD-clusters in which cluster neurons are in zero-lag
synchronization. For complex external stimuli, the number of clusters can be
any common divisor. The synchronized mode and the transients to synchronization
pinpoint the type of external stimuli. The findings, supported by an
information mixing argument and simulations of Hodgkin Huxley population
dynamic networks with unidirectional connectivity and synaptic noise, call for
reexamining sources of correlated activity in cortex and shorter information
processing time scales.Comment: 8 pges, 6 figure
Nonequilibrium critical behavior of a species coexistence model
A biologically motivated model for spatio-temporal coexistence of two
competing species is studied by mean-field theory and numerical simulations. In
d>1 dimensions the phase diagram displays an extended region where both species
coexist, bounded by two second-order phase transition lines belonging to the
directed percolation universality class. The two transition lines meet in a
multicritical point, where a non-trivial critical behavior is observed.Comment: 11 page
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