1,873 research outputs found
A continuous model of ant foraging with pheromones and trail formation
We propose and numerically analyze a PDE model of ant foraging behavior. Ant
foraging is a prime example of individuals following simple behavioral rules
based on local information producing complex, organized and ``intelligent''
strategies at the population level. One of its main aspects is the widespread
use of pheromones, which are chemical compounds laid by the ants used to
attract other ants to a food source. In this work, we consider a continuous
description of a population of ants and simulate numerically the foraging
behavior using a system of PDEs of chemotaxis type. We show that, numerically,
this system accurately reproduces observed foraging behavior, such as trail
formation and efficient removal of food sources.Comment: Conference proceeding
Analysis of a chemotaxis system modeling ant foraging
In this paper we analyze a system of PDEs recently introduced in [P. Amorim,
{\it Modeling ant foraging: a {chemotaxis} approach with pheromones and trail
formation}], in order to describe the dynamics of ant foraging. The system is
made of convection-diffusion-reaction equations, and the coupling is driven by
chemotaxis mechanisms. We establish the well-posedness for the model, and
investigate the regularity issue for a large class of integrable data. Our main
focus is on the (physically relevant) two-dimensional case with boundary
conditions, where we prove that the solutions remain bounded for all times. The
proof involves a series of fine \emph{a priori} estimates in Lebesgue spaces.Comment: 39 page
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