585 research outputs found
On the Gaussian approximation for master equations
We analyze the Gaussian approximation as a method to obtain the first and
second moments of a stochastic process described by a master equation. We
justify the use of this approximation with ideas coming from van Kampen's
expansion approach (the fact that the probability distribution is Gaussian at
first order). We analyze the scaling of the error with a large parameter of the
system and compare it with van Kampen's method. Our theoretical analysis and
the study of several examples shows that the Gaussian approximation turns out
to be more accurate. This could be specially important for problems involving
stochastic processes in systems with a small number of particles
Exact solution of a stochastic protein dynamics model with delayed degradation
We study a stochastic model of protein dynamics that explicitly includes
delay in the degradation. We rigorously derive the master equation for the
processes and solve it exactly. We show that the equations for the mean values
obtained differ from others intuitively proposed and that oscillatory behavior
is not possible in this system. We discuss the calculation of correlation
functions in stochastic systems with delay, stressing the differences with
Markovian processes. The exact results allow to clarify the interplay between
stochasticity and delay
On the effect of heterogeneity in stochastic interacting-particle systems
We study stochastic particle systems made up of heterogeneous units. We
introduce a general framework suitable to analytically study this kind of
systems and apply it to two particular models of interest in economy and
epidemiology. We show that particle heterogeneity can enhance or decrease the
collective fluctuations depending on the system, and that it is possible to
infer the degree and the form of the heterogeneity distribution in the system
by measuring only global variables and their fluctuations
Ordering dynamics in the voter model with aging
The voter model with memory-dependent dynamics is theoretically and
numerically studied at the mean-field level. The `internal age', or time an
individual spends holding the same state, is added to the set of binary states
of the population, such that the probability of changing state (or activation
probability ) depends on this age. A closed set of integro-differential
equations describing the time evolution of the fraction of individuals with a
given state and age is derived, and from it analytical results are obtained
characterizing the behavior of the system close to the absorbing states. In
general, different age-dependent activation probabilities have different
effects on the dynamics. When the activation probability is an increasing
function of the age , the system reaches a steady state with coexistence of
opinions. In the case of aging, with being a decreasing function, either
the system reaches consensus or it gets trapped in a frozen state, depending on
the value of (zero or not) and the velocity of approaching
. Moreover, when the system reaches consensus, the time ordering of
the system can be exponential () or power-law like ().
Exact conditions for having one or another behavior, together with the
equations and explicit expressions for the exponents, are provided
Divergent Time Scale in Axelrod Model Dynamics
We study the evolution of the Axelrod model for cultural diversity. We
consider a simple version of the model in which each individual is
characterized by two features, each of which can assume q possibilities. Within
a mean-field description, we find a transition at a critical value q_c between
an active state of diversity and a frozen state. For q just below q_c, the
density of active links between interaction partners is non-monotonic in time
and the asymptotic approach to the steady state is controlled by a time scale
that diverges as (q-q_c)^{-1/2}.Comment: 4 pages, 5 figures, 2-column revtex4 forma
Non-universal results induced by diversity distribution in coupled excitable systems
We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity distribution with well defined moments. Singularly, for the Lorentzian distribution (widely used in Kuramoto-like systems) the transition is not present. This warns about the use of Lorentzian distributions to understand the generic properties of coupled oscillators.We acknowledge financial support by the MICINN (Spain) and FEDER (EU) through
project FIS2007-60327. L.F.L. is supported by the
JAEPredoc program of CSIC.Peer reviewe
Non-universal results induced by diversity distribution in coupled excitable systems
We consider a system of globally coupled active rotators near the excitable
regime. The system displays a transition to a state of collective firing
induced by disorder. We show that this transition is found generically for any
diversity distribution with well defined moments. Singularly, for the
Lorentzian distribution (widely used in Kuramoto-like systems) the transition
is not present. This warns about the use of Lorentzian distributions to
understand the generic properties of coupled oscillators
Coherence Resonance in Chaotic Systems
We show that it is possible for chaotic systems to display the main features
of coherence resonance. In particular, we show that a Chua model, operating in
a chaotic regime and in the presence of noise, can exhibit oscillations whose
regularity is optimal for some intermediate value of the noise intensity. We
find that the power spectrum of the signal develops a peak at finite frequency
at intermediate values of the noise. These are all signatures of coherence
resonance. We also experimentally study a Chua circuit and corroborate the
above simulation results. Finally, we analyze a simple model composed of two
separate limit cycles which still exhibits coherence resonance, and show that
its behavior is qualitatively similar to that of the chaotic Chua systemComment: 4 pages (including 4 figures) LaTeX fil
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