相关论文: The L\'evy flight foraging hypothesis: comparison …
How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extended versions of three well-known models of two competing species with unequal diffusivities. Though…
This paper studies the optimal unmanned aerial vehicle (UAV) placement problem for wireless networking. The UAV operates as a flying wireless relay to provide coverage extension for a base station (BS) and deliver capacity boost to a user…
The L\'evy flight foraging hypothesis asserts that biological organisms have evolved to employ (truncated) L\'evy flight searches due to such strategies being more efficient than those based on Brownian motion. However, we provide here a…
In this paper we propose and advocate the use of the so called L\'evy flights as a driving mechanism for a class of stochastic optimization computations. This proposal, for some reasons overlooked until now, is - in author's opinion - very…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at $x_0\geq0$, where successive jumps are drawn independently…
The foraging behavior of animals is a paradigm of target search in nature. Understanding which foraging strategies are optimal and how animals learn them are central challenges in modeling animal foraging. While the question of optimality…
We study the dynamics of predator-prey systems where prey are confined to a single region of space and where predators move randomly according to a power-law (L\'evy) dispersal kernel. Site fidelity, an important feature of animal…
Brownian motion is widely used as a paradigmatic model of diffusion in equilibrium media throughout the physical, chemical, and biological sciences. However, many real world systems, particularly biological ones, are intrinsically…
L\'{e}vy flights is a random walk where the step-lengths have a probability distribution that is heavy-tailed. It has been shown that L\'{e}vy flights can maximize the efficiency of resource searching in uncertain environments, and also…
Target shape, not just size, plays a pivotal role in determining detectability during random search. We analyze intermittent L\'evy walks in three dimensions, and mathematically prove that the widely observed Cauchy strategy (L\'evy…
We refute here the concernes raised in the Comment of our letter. This reply states clearly the validity range of our results and shows that the optimality of inverse-square Levy walks at the basis of the Levy flight foraging hypothesis is…
We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…
We analyze the movement of a starving forager on a one-dimensional periodic lattice, where each location contains one unit of food. As the forager lands on sites with food, it consumes the food, leaving the sites empty. If the forager lands…
What is the most efficient search strategy for the random located target sites subject to the physical and biological constraints? Previous results suggested the L\'evy flight is the best option to characterize this optimal problem,…
Autonomous robots are commonly tasked with the problem of area exploration and search for certain targets or artifacts of interest to be tracked. Traditionally, the problem formulation considered is that of complete search and thus -…
Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce randomly distributed resources, but a less explored alternative is that this behaviour may result from the…
In this paper, preys with stochastic evasion policies are considered. The stochasticity adds unpredictable changes to the prey's path for avoiding predator's attacks. The prey's cost function is composed of two terms balancing the…
We introduce a formalism of fractional diffusion on networks based on a fractional Laplacian matrix that can be constructed directly from the eigenvalues and eigenvectors of the Laplacian matrix. This fractional approach allows random walks…
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 distribution in a given box. We…