100 research outputs found
Ergodicity breaking and lack of a typical waiting time in area-restricted search of avian predators
Movement tracks of wild animals frequently fit models of anomalous rather
than simple diffusion, mostly reported as ergodic superdiffusive motion
combining area-restricted search within a local patch and larger-scale
commuting between patches, as highlighted by the L\'evy walk paradigm. Since
L\'evy walks are scale invariant, superdiffusive motion is also expected within
patches, yet investigation of such local movements has been precluded by the
lack of accurate high-resolution data at this scale. Here, using rich
high-resolution movement datasets ( localizations) from 70
individuals and continuous-time random walk modeling, we found subdiffusive
behavior and ergodicity breaking in the localized movement of three species of
avian predators. Small-scale, within-patch movement was qualitatively
different, not inferrable and separated from large-scale inter-patch movement
via a clear phase transition. Local search is characterized by long
power-law-distributed waiting times with diverging mean, giving rise to
ergodicity breaking in the form of considerable variability uniquely observed
at this scale. This implies that wild animal movement is scale specific rather
than scale free, with no typical waiting time at the local scale. Placing these
findings in the context of the static-ambush to mobile-cruise foraging
continuum, we verify predictions based on the hunting behavior of the study
species and the constraints imposed by their prey.Comment: 27 pages, 8 figure
Analysis of a stochastic delay competition system driven by Lévy noise under regime switching
This paper is concerned with a stochastic delay competition system driven by Lévy noise under regime switching. Both the existence and uniqueness of the global positive solution are examined. By comparison theorem, sufficient conditions for extinction and non-persistence in the mean are obtained. Some discussions are made to demonstrate that the different environment factors have significant impacts on extinction. Furthermore, we show that the global positive solution is stochastically ultimate boundedness under some conditions, and an important asymptotic property of system is given. In the end, numerical simulations are carried out to illustrate our main results
First passage time moments of asymmetric L\'evy flights
We investigate the first-passage dynamics of symmetric and asymmetric L\'evy
flights in a semi-infinite and bounded intervals. By solving the
space-fractional diffusion equation, we analyse the fractional-order moments of
the first-passage time probability density function for different values of the
index of stability and the skewness parameter. A comparison with results using
the Langevin approach to L\'evy flights is presented. For the semi-infinite
domain, in certain special cases analytic results are derived explicitly, and
in bounded intervals a general analytical expression for the mean first-passage
time of L\'evy flights with arbitrary skewness is presented. These results are
complemented with extensive numerical analyses.Comment: 47 pages, 13 figures, IOP LaTe
Slow manifolds for stochastic koper models with stable Lévy noises
The Koper model is a vector field in which the differential equations describe the electrochemical oscillations appearing in diffusion processes. This work focuses on the understanding of the slow dynamics of a stochastic Koper model perturbed by stable Lévy noise. We establish the slow manifold for a stochastic Koper model with stable Lévy noise and verify exponential tracking properties. We also present two practical examples to demonstrate the analytical results with numerical simulations
Intermittent search strategies
This review examines intermittent target search strategies, which combine
phases of slow motion, allowing the searcher to detect the target, and phases
of fast motion during which targets cannot be detected. We first show that
intermittent search strategies are actually widely observed at various scales.
At the macroscopic scale, this is for example the case of animals looking for
food ; at the microscopic scale, intermittent transport patterns are involved
in reaction pathway of DNA binding proteins as well as in intracellular
transport. Second, we introduce generic stochastic models, which show that
intermittent strategies are efficient strategies, which enable to minimize the
search time. This suggests that the intrinsic efficiency of intermittent search
strategies could justify their frequent observation in nature. Last, beyond
these modeling aspects, we propose that intermittent strategies could be used
also in a broader context to design and accelerate search processes.Comment: 72 pages, review articl
Biological control of the chestnut gall wasp with \emph{T. sinensis}: a mathematical model
The Asian chestnut gall wasp \emph{Dryocosmus kuriphilus}, native of China,
has become a pest when it appeared in Japan, Korea, and the United States. In
Europe it was first found in Italy, in 2002. In 1982 the host-specific
parasitoid \emph{Torymus sinensis} was introduced in Japan, in an attempt to
achieve a biological control of the pest. After an apparent initial success,
the two species seem to have locked in predator-prey cycles of decadal length.
We have developed a spatially explicit mathematical model that describes the
seasonal time evolution of the adult insect populations, and the competition
for finding egg deposition sites. In a spatially homogeneous situation the
model reduces to an iterated map for the egg density of the two species. While
the map would suggest, for realistic parameters, that both species should
become locally extinct (somewhat corroborating the hypothesis of biological
control), the full model, for the same parameters, shows that the introduction
of \emph{T. sinensis} sparks a traveling wave of the parasitoid population that
destroys the pest on its passage. Depending on the value of the diffusion
coefficients of the two species, the pest can later be able to re-colonize the
empty area left behind the wave. When this occurs the two populations do not
seem to attain a state of spatial homogeneity, but produce an ever-changing
pattern of traveling waves
Statistical-thermodynamical foundations of anomalous diffusion
It is shown that Tsallis' generalized statistics provides a natural frame for
the statistical-thermodynamical description of anomalous diffusion. Within this
generalized theory, a maximum-entropy formalism makes it possible to derive a
mathematical formulation for the mechanisms that underly Levy-like
superdiffusion, and for solving the nonlinear Fokker-Planck equation.Comment: 13 pages, 8 figures; to appear in special issue of Braz. J. Phys. as
invited revie
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