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Math Biosci

Title:		Mathematical model for path selection by ants between nest and food source
Author(s):		Bodnar M; Okinczyc N; Vela-Perez M;
Address:		"Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland. Electronic address: mbodnar@mimuw.edu.pl. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland. Electronic address: n.okinczyc@gmail.com. Universidad Europea de Madrid, C/ Tajo, Villaviciosa de Odon, Madrid 28670, Spain; Service de Physique de l'Etat Condense, CEA-Saclay, 91191 Gif-sur-Yvette, France; Instituto de Ciencias Matematicas, (CSIC), C/ Nicolas Cabrera 15, 28049 Madrid, Spain. Electronic address: mvp_es@yahoo.es"
Journal Title:		Math Biosci
Year:		2017
Volume:		20161212
Issue:
Page Number:		14 - 24
DOI:		10.1016/j.mbs.2016.12.002
ISSN/ISBN:		1879-3134 (Electronic) 0025-5564 (Linking)
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"
Keywords:		"Animals Ants/*physiology Behavior, Animal/*physiology *Models, Theoretical Ant foraging Reinforced random walks Stochastic processes Transport networks;"
Notes:		"MedlineBodnar, Marek Okinczyc, Natalia Vela-Perez, M eng Research Support, Non-U.S. Gov't 2016/12/17 Math Biosci. 2017 Mar; 285:14-24. doi: 10.1016/j.mbs.2016.12.002. Epub 2016 Dec 12"