Fractional order Orlicz-Sobolev spaces.
Expositor: Julián F. Bonder
Instituição: Univ de Buenos Aires
Data e Horário: 13/9/2017 | 17:00hs
RESUMO: We propose and analyze different models of ant foraging behavior. Ant foraging is among the most interesting behaviors in the animal kingdom, and 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. We consider first 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 reproduces some observed foraging behavior, such as trail formation. Furthermore, in collaboration with R. Alonso (PUC-RJ) and Th. Goudon (INRIA), we present a thorough mathematical analysis of a version of the model. After a critical analysis of this model, we propose an individual-based model which takes into account the rules for individual response to pheromones. For this model, we present some mathematical results and collective simulations showing spontaneous trail formation.