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J Math Biol

Title:		An ant navigation model based on Weber's law
Author(s):		Amorim P; Goudon T; Peruani F;
Address:		"Instituto de Matematica, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Centro de Tecnologia - Bloco C, Cidade Universitaria - Ilha do Fundao, Caixa Postal 68530, 21941-909, Rio de Janeiro, RJ, Brasil. paulo@im.ufrj.br. Inria, CNRS, LJAD, Universite Cote d'Azur, Nice, France. CNRS, LJAD, Universite Cote d'Azur, Nice, France"
Journal Title:		J Math Biol
Year:		2019
Volume:		20181009
Issue:		4
Page Number:		943 - 984
DOI:		10.1007/s00285-018-1298-7
ISSN/ISBN:		1432-1416 (Electronic) 0303-6812 (Linking)
Abstract:		"We analyze an ant navigation model based on Weber's law, where the ants move across a pheromone landscape sensing the area using two antennae. The key parameter of the model is the angle [Formula: see text] representing the span of the ant's sensing area. We show that when [Formula: see text] ants are able to follow (straight) pheromone trails proving that for initial conditions close to the trail, there exists a Lyapunov function that ensures ant trajectories converge on and follow the pheromone trail, with these solutions being locally asymptotically stable. Furthermore, we indicate that the features of the ant trajectories such as convergence speed or oscillation wave length are controlled by the angle [Formula: see text]. For [Formula: see text], we present numerical evidence that indicates that ants are unable to follow pheromone trails. We also assess our model by comparing it to previous experimental results, showing that the solutions' behavior falls into biologically meaningful ranges. Our work provides solid mathematical support for experimental studies where it was found that ant perception follows a Weber's law, by proving that such models lead to the desired robust and stable trail following"
Keywords:		"Animals Ants/*physiology Arthropod Antennae/physiology Behavior, Animal/physiology Computational Biology Feeding Behavior/physiology Linear Models Locomotion/physiology Mathematical Concepts *Models, Biological Pheromones/physiology Animal movement Ant na;"
Notes:		"MedlineAmorim, Paulo Goudon, Thierry Peruani, Fernando eng 442960/2014-0/Conselho Nacional de Desenvolvimento Cientifico e Tecnologico/International 202.867/2015/Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro/International Research Support, Non-U.S. Gov't Germany 2018/10/12 J Math Biol. 2019 Mar; 78(4):943-984. doi: 10.1007/s00285-018-1298-7. Epub 2018 Oct 9"