Related papers: Optimal L\'{e}vy-flight foraging in a finite lands…
Our study focuses on analyzing the behavior of a stochastic predator-prey model with a time delay and logistic growth of prey, influenced by L\'{e}vy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive…
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…
This paper investigates a class of stochastic Logistic harvesting models driven by tempered stable processes, with a one-sided power-law L\'evy measure. We establish threshold conditions for population extinction and persistence, prove the…
Thanks to recent technological advances, it is now possible to track with an unprecedented precision and for long periods of time the movement patterns of many living organisms in their habitat. The increasing amount of data available on…
Consider a team of agents in the plane searching for and visiting target points that appear in a bounded environment according to a stochastic renewal process with a known absolutely continuous spatial distribution. Agents must detect…
We consider diffusive motion of a particle performing a random walk with L\'evy distributed jump lengths and subject to resetting mechanism bringing the walker to an initial position at uniformly distributed times. In the limit of infinite…
Two the most common tasks for autonomous mobile robots is to explore the environment and locate a target. %In the last case, the objective is either to find a target in the shortest time possible or, alternatively, to find %as many targets…
In this study, we couple a population dynamics model with a model for optimal foraging to study the interdependence between individual-level cost-benefits and population-scale dynamics. Specifically, we study the logistic growth model,…
An efficient search algorithm is very crucial in robotic area, especially for exploration missions, where the target availability is unknown and the condition of the environment is highly unpredictable. In a very large environment, it is…
We study the fate of a forager who searches for food performing a random walk on lattices. The forager consumes the available food on the site it visits and leaves it depleted but can survive up to $S$ steps without food. We introduce the…
Recent works have explored the properties of L\'evy flights with resetting in one-dimensional domains and have reported the existence of phase transitions in the phase space of parameters which minimizes the Mean First Passage Time (MFPT)…
We measured mobility patterns that describe walking trajectories of individual Me'Phaa peasants searching and collecting fuelwood in the forests of "La Monta\~na de Guerrero" in Mexico. These one-day excursions typically follow a mixed…
Foraging is a fundamental behavior as animals' search for food is crucial for their survival. Patch leaving is a canonical foraging behavior, but classic theoretical conceptions of patch leaving decisions lack some key naturalistic details.…
Motile organisms often use finite spatial perception of their surroundings to navigate and search their habitats. Yet standard models of search are usually based on purely local sensory information. To model how a finite perceptual horizon…
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…
A canonical foraging task is the patch-leaving problem, in which a forager must decide to leave a current resource in search for another. Theoretical work has derived optimal strategies for when to leave a patch, and experiments have tested…
The paper proposes a novel nature-inspired technique of optimization. It mimics the perching nature of eagles and uses mathematical formulations to introduce a new addition to metaheuristic algorithms. The nature of the proposed algorithm…
L\'{e}vy robotic systems combine superdiffusive random movement with emergent collective behaviour from local communication and alignment in order to find rare targets or track objects. In this article we derive macroscopic fractional PDE…
In this paper, we analyze the dynamics of a multi-species fisheries system in the presence of harvesting. We solve the problem of finding the optimal harvesting strategy for a mid-term horizon with a fixed final stock of each species, while…
In environments with scarce resources, adopting the right search strategy can make the difference between succeeding and failing, even between life and death. At different scales, this applies to molecular encounters in the cell cytoplasm,…