The movement of a forager: Strategies for the efficient use of resources

We study a simple model of a foraging animal that modifies the substrate on which it moves. This substrate provides its only resource, and the forager manage it by taking a limited portion at each visited site. The resource recovers its value after the visit following a relaxation law. We study different scenarios to analyze the efficiency of the managing strategy, corresponding to control the bite size. We observe the non trivial emergence of a home range, that is visited in a periodic way. The duration of the corresponding cycles and the transient until it emerges is affected by the bite size. Our results show that the most efficient use of the resource, measured as the balance between gathering and travelled distance, corresponds to foragers that take larger portions but without exhausting the resource. We also analyze the use of space determining the number of attractors of the dynamics, and we observe that it depends on the bite size and the recovery time of the resource.