17,027 research outputs found
Noise-Induced Spatial Pattern Formation in Stochastic Reaction-Diffusion Systems
This paper is concerned with stochastic reaction-diffusion kinetics governed
by the reaction-diffusion master equation. Specifically, the primary goal of
this paper is to provide a mechanistic basis of Turing pattern formation that
is induced by intrinsic noise. To this end, we first derive an approximate
reaction-diffusion system by using linear noise approximation. We show that the
approximated system has a certain structure that is associated with a coupled
dynamic multi-agent system. This observation then helps us derive an efficient
computation tool to examine the spatial power spectrum of the intrinsic noise.
We numerically demonstrate that the result is quite effective to analyze
noise-induced Turing pattern. Finally, we illustrate the theoretical mechanism
behind the noise-induced pattern formation with a H2 norm interpretation of the
multi-agent system
Effects of external global noise on the catalytic CO oxidation on Pt(110)
Oxidation reaction of CO on a single platinum crystal is a reaction-diffusion
system that may exhibit bistable, excitable, and oscillatory behavior. We
studied the effect of a stochastic signal artificially introduced into the
system through the partial pressure of CO. First, the external signal is
employed as a turbulence suppression tool, and second, it modifies the
boundaries in the bistable transition between the CO and oxygen covered phases.
Experiments using photoemission electron microscopy (PEEM) together with
numerical simulations performed with the Krischer-Eiswirth-Ertl (KEE) model are
presented.Comment: 15 pages, 7 figures, accepted in J. Chem. Phy
Patchiness and Demographic Noise in Three Ecological Examples
Understanding the causes and effects of spatial aggregation is one of the
most fundamental problems in ecology. Aggregation is an emergent phenomenon
arising from the interactions between the individuals of the population, able
to sense only -at most- local densities of their cohorts. Thus, taking into
account the individual-level interactions and fluctuations is essential to
reach a correct description of the population. Classic deterministic equations
are suitable to describe some aspects of the population, but leave out features
related to the stochasticity inherent to the discreteness of the individuals.
Stochastic equations for the population do account for these
fluctuation-generated effects by means of demographic noise terms but, owing to
their complexity, they can be difficult (or, at times, impossible) to deal
with. Even when they can be written in a simple form, they are still difficult
to numerically integrate due to the presence of the "square-root" intrinsic
noise. In this paper, we discuss a simple way to add the effect of demographic
stochasticity to three classic, deterministic ecological examples where
aggregation plays an important role. We study the resulting equations using a
recently-introduced integration scheme especially devised to integrate
numerically stochastic equations with demographic noise. Aimed at scrutinizing
the ability of these stochastic examples to show aggregation, we find that the
three systems not only show patchy configurations, but also undergo a phase
transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy
Resonance and frequency-locking phenomena in spatially extended phytoplankton-zooplankton system with additive noise and periodic forces
In this paper, we present a spatial version of phytoplankton-zooplankton
model that includes some important factors such as external periodic forces,
noise, and diffusion processes. The spatially extended
phytoplankton-zooplankton system is from the original study by Scheffer [M
Scheffer, Fish and nutrients interplay determines algal biomass: a minimal
model, Oikos \textbf{62} (1991) 271-282]. Our results show that the spatially
extended system exhibit a resonant patterns and frequency-locking phenomena.
The system also shows that the noise and the external periodic forces play a
constructive role in the Scheffer's model: first, the noise can enhance the
oscillation of phytoplankton species' density and format a large clusters in
the space when the noise intensity is within certain interval. Second, the
external periodic forces can induce 4:1 and 1:1 frequency-locking and spatially
homogeneous oscillation phenomena to appear. Finally, the resonant patterns are
observed in the system when the spatial noises and external periodic forces are
both turned on. Moreover, we found that the 4:1 frequency-locking transform
into 1:1 frequency-locking when the noise intensity increased. In addition to
elucidating our results outside the domain of Turing instability, we provide
further analysis of Turing linear stability with the help of the numerical
calculation by using the Maple software. Significantly, oscillations are
enhanced in the system when the noise term presents. These results indicate
that the oceanic plankton bloom may partly due to interplay between the
stochastic factors and external forces instead of deterministic factors. These
results also may help us to understand the effects arising from undeniable
subject to random fluctuations in oceanic plankton bloom.Comment: Some typos errors are proof, and some strong relate references are
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