4,398 research outputs found
Sustained plankton blooms under open chaotic flows
We consider a predator-prey model of planktonic population dynamics, of
excitable character, living in an open and chaotic fluid flow, i.e., a state of
fluid motion in which fluid trajectories are unbounded but a chaotic region
exists that is restricted to a localized area. Despite that excitability is a
transient phenomenon and that fluid trajectories are continuously leaving the
system, there is a regime of parameters where the excitation remains
permanently in the system, given rise to a persistent plankton bloom. This
regime is reached when the time scales associated to fluid stirring become
slower than the ones associated to biological growth.Comment: 14 pages, 3 figure
Spatial Patterns in Chemically and Biologically Reacting Flows
We present here a number of processes, inspired by concepts in Nonlinear
Dynamics such as chaotic advection and excitability, that can be useful to
understand generic behaviors in chemical or biological systems in fluid flows.
Emphasis is put on the description of observed plankton patchiness in the sea.
The linearly decaying tracer, and excitable kinetics in a chaotic flow are
mainly the models described. Finally, some warnings are given about the
difficulties in modeling discrete individuals (such as planktonic organisms) in
terms of continuous concentration fields.Comment: 41 pages, 10 figures; To appear in the Proceedings of the 2001 ISSAOS
School on 'Chaos in Geophysical Flows
Spatial patterns of competing random walkers
We review recent results obtained from simple individual-based models of
biological competition in which birth and death rates of an organism depend on
the presence of other competing organisms close to it. In addition the
individuals perform random walks of different types (Gaussian diffusion and
L\'{e}vy flights). We focus on how competition and random motions affect each
other, from which spatial instabilities and extinctions arise. Under suitable
conditions, competitive interactions lead to clustering of individuals and
periodic pattern formation. Random motion has a homogenizing effect and then
delays this clustering instability. When individuals from species differing in
their random walk characteristics are allowed to compete together, the ones
with a tendency to form narrower clusters get a competitive advantage over the
others. Mean-field deterministic equations are analyzed and compared with the
outcome of the individual-based simulations.Comment: 38 pages, including 6 figure
Species clustering in competitive Lotka-Volterra models
We study the properties of Lotka-Volterra competitive models in which the
intensity of the interaction among species depends on their position along an
abstract niche space through a competition kernel. We show analytically and
numerically that the properties of these models change dramatically when the
Fourier transform of this kernel is not positive definite, due to a pattern
forming instability. We estimate properties of the species distributions, such
as the steady number of species and their spacings, for different types of
kernels.Comment: 4 pages, 3 figure
Noise rectification in quasigeostrophic forced turbulence
We study the appearance of large scale mean motion sustained by stochastic
forcing on a rotating fluid (in the quasigeostrophic approximation) flowing
over topography. As in other noise rectification phenomena, the effect requires
nonlinearity and absence of detailed balance to occur. By application of an
analytical coarse graining procedure we identify the physical mechanism
producing such effect: It is a forcing coming from the small scales that
manifests in a change in the effective viscosity operator and in the effective
noise statistical properties.Comment: 4 pages revtex, including 5 figures. Related material at
http://www.imedea.uib.es/Nonlinear and http://www.imedea.uib.es/Oceanography
Figure 4 replaced by a slightly better on
The noisy Hegselmann-Krause model for opinion dynamics
In the model for continuous opinion dynamics introduced by Hegselmann and
Krause, each individual moves to the average opinion of all individuals within
an area of confidence. In this work we study the effects of noise in this
system. With certain probability, individuals are given the opportunity to
change spontaneously their opinion to another one selected randomly inside the
opinion space with different rules. If the random jump does not occur,
individuals interact through the Hegselmann-Krause's rule. We analyze two
cases, one where individuals can carry out opinion random jumps inside the
whole opinion space, and other where they are allowed to perform jumps just
inside a small interval centered around the current opinion. We found that
these opinion random jumps change the model behavior inducing interesting
phenomena. Using pattern formation techniques, we obtain approximate analytical
results for critical conditions of opinion cluster formation. Finally, we
compare the results of this work with the noisy version of the Deffuant et al.
model for continuous-opinion dynamics
Vegetation pattern formation in semiarid systems without facilitative mechanisms
Regular vegetation patterns in semiarid ecosystems are believed to arise from
the interplay between long-range competition and facilitation processes acting
at smaller distances. We show that, under rather general conditions, long-range
competition alone may be enough to shape these patterns. To this end we propose
a simple, general model for the dynamics of vegetation, which includes only
long-range competition between plants. Competition is introduced through a
nonlocal term, where the kernel function quantifies the intensity of the
interaction. We recover the full spectrum of spatial structures typical of
vegetation models that also account for facilitation in addition to
competition.Comment: 21 pages, 3 figure
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