23 research outputs found
Universality of residence-time distributions in non-adiabatic stochastic resonance
We present mathematically rigorous expressions for the residence-time and
first-passage-time distributions of a periodically forced Brownian particle in
a bistable potential. For a broad range of forcing frequencies and amplitudes,
the distributions are close to periodically modulated exponential ones.
Remarkably, the periodic modulations are governed by universal functions,
depending on a single parameter related to the forcing period. The behaviour of
the distributions and their moments is analysed, in particular in the low- and
high-frequency limits.Comment: 8 pages, 1 figure New version includes distinction between
first-passage-time and residence-time distribution
Fast Monte Carlo simulations and singularities in the probability distributions of non-equilibrium systems
A numerical technique is introduced that reduces exponentially the time
required for Monte Carlo simulations of non-equilibrium systems. Results for
the quasi-stationary probability distribution in two model systems are compared
with the asymptotically exact theory in the limit of extremely small noise
intensity. Singularities of the non-equilibrium distributions are revealed by
the simulations.Comment: 4 pages, 4 figure
Large rare fluctuations in systems with delayed dissipation
We study the probability distribution and the escape rate in systems with
delayed dissipation that comes from the coupling to a thermal bath. To
logarithmic accuracy in the fluctuation intensity, the problem is reduced to a
variational problem. It describes the most probable fluctuational paths, which
are given by acausal equations due to the delay. In thermal equilibrium, the
most probable path passing through a remote state has time reversal symmetry,
even though one cannot uniquely define a path that starts from a state with
given system coordinate and momentum. The corrections to the distribution and
the escape activation energy for small delay and small noise correlation time
are obtained in the explicit form.Comment: 9 page
Scaling and crossovers in activated escape near a bifurcation point
Near a bifurcation point a system experiences critical slowing down. This
leads to scaling behavior of fluctuations. We find that a periodically driven
system may display three scaling regimes and scaling crossovers near a
saddle-node bifurcation where a metastable state disappears. The rate of
activated escape scales with the driving field amplitude as , where is the bifurcational value of . With
increasing field frequency the critical exponent changes from
for stationary systems to a dynamical value and then again to
. The analytical results are in agreement with the results of
asymptotic calculations in the scaling region. Numerical calculations and
simulations for a model system support the theory.Comment: 18 page
Steady states in a structured epidemic model with Wentzell boundary condition
We introduce a nonlinear structured population model with diffusion in the
state space. Individuals are structured with respect to a continuous variable
which represents a pathogen load. The class of uninfected individuals
constitutes a special compartment that carries mass, hence the model is
equipped with generalized Wentzell (or dynamic) boundary conditions. Our model
is intended to describe the spread of infection of a vertically transmitted
disease, for example Wolbachia in a mosquito population. Therefore the
(infinite dimensional) nonlinearity arises in the recruitment term. First we
establish global existence of solutions and the Principle of Linearised
Stability for our model. Then, in our main result, we formulate simple
conditions, which guarantee the existence of non-trivial steady states of the
model. Our method utilizes an operator theoretic framework combined with a
fixed point approach. Finally, in the last section we establish a sufficient
condition for the local asymptotic stability of the positive steady state
Disease extinction in the presence of non-Gaussian noise
We investigate stochastic extinction in an epidemic model and the impact of
random vaccinations in large populations. We show that, in the absence of
vaccinations, the effective entropic barrier for extinction displays scaling
with the distance to the bifurcation point, with an unusual critical exponent.
Even a comparatively weak Poisson-distributed vaccination leads to an
exponential increase in the extinction rate, with the exponent that strongly
depends on the vaccination parameters.Comment: Accepted for publication to PR