相关论文: The L\'evy flight foraging hypothesis: comparison …

In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…

The search for hidden targets is a fundamental problem in many areas of science, engineering, and other fields. Studies of search processes often adopt a probabilistic framework, in which a searcher randomly explores a spatial domain for a…

Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…

The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…

Cooperation among individuals has been key to sustaining societies. However, natural selection favors defection over cooperation. Cooperation can be favored when the mobility of individuals allows cooperators to form a cluster (or group).…

A combined dynamics consisting of Brownian motion and L\'evy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of…

We consider the model of spatially distributed population consisting of two species with "\textsl{predator\,--\,prey}" interaction; each of the species occupies two stations. Transfer of individuals between the stations (migration) is not…

We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…

We study the kinetics for the search of an immobile target by randomly moving searchers that detect it only upon encounter. The searchers perform intermittent random walks on a one-dimensional lattice. Each searcher can step on a nearest…

We consider one dimensional diffusive search strategies subjected to external potentials. The location of a single target is drawn from a given probability density function (PDF) $f_G(x)$ and is fixed for each stochastic realization of the…

The diffusion of a walk in the presence of traps is investigated. Different diffusion regimes are obtained considering the magnitude of the fluctuations in waiting times and jump distances. A constant velocity during the jump motion is…

We study the probability distribution function (pdf) of the position of a L\'evy flight of index 0<\alpha<2 in presence of an absorbing wall at the origin. The solution of the associated fractional Fokker-Planck equation can be constructed…

Following some recent works, we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a…

In this article, we study the optimization of resource distributions in a one-dimensional logistic diffusive model. The goal is to determine a distribution on a bounded one-dimensional domain that maximizes the total population at…

In natural foraging, many organisms seem to perform two different types of motile search: directed search (taxis) and random search. The former is observed when the environment provides cues to guide motion towards a target. The latter…

Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually…

In this article, we consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources…

The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…

We study a simple model of a foraging animal that modifies the substrate on which it moves. This substrate provides its only resource, and the forager manage it by taking a limited portion at each visited site. The resource recovers its…

We introduce a model of traveling agents ({\it e.g.} frugivorous animals) who feed on randomly located vegetation patches and disperse their seeds, thus modifying the spatial distribution of resources in the long term. It is assumed that…