title: Mathematical model for path selection by ants between nest and food source.
abstract: Several models have been proposed to describe the behavior of ants when moving from nest to food sources. Most of these studies where based on numerical simulations with no mathematical justification. In this paper, we propose a mechanism for the formation of paths of minimal length between two points by a collection of individuals undergoing reinforced random walks taking into account not only the lengths of the paths but also the angles (connected to the preference of ants to move along straight lines). Our model involves reinforcement (pheromone accumulation), persistence (tendency to preferably follow straight directions in absence of any external effect) and takes into account the bifurcation angles of each edge (represented by a probability of willingness of choosing the path with the smallest angle). We describe analytically the results for 2 ants and different path lengths and numerical simulations for several ants.
authors.affiliation: Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland. Electronic address: mbodnar@mimuw.edu.pl.
authors.forename: Marek
authors.initials: M
authors.lastname: Bodnar
authors.affiliation: Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland. Electronic address: n.okinczyc@gmail.com.
authors.forename: Natalia
authors.initials: N
authors.lastname: Okińczyc
authors.affiliation: Universidad Europea de Madrid, C/ Tajo, Villaviciosa de Odón, Madrid 28670, Spain; Service de Physique de l'Etat Condensé, CEA-Saclay, 91191 Gif-sur-Yvette, France; Instituto de Ciencias Matemáticas, (CSIC), C/ Nicolás Cabrera 15, 28049 Madrid, Spain. Electronic address: mvp_es@yahoo.es.
authors.forename: M
authors.initials: M
authors.lastname: Vela-Pérez
mesh_terms: D000818:Animals; D001000:Ants / Q000502:physiology*; D001522:Behavior, Animal / Q000502:physiology*; D008962:Models, Theoretical
keywords: Ant foraging; Reinforced random walks; Stochastic processes; Transport networks