Fuzzy Modeling of Reoccupation of a Leaf-cutting Ants' Trail

In this paper we model the reoccupation of a trail by leaf-cutting ants. The mathematical modeling consists in studying the leaf-cutting ants' displacement towards an attraction area and their return to the nest. To carry out this research, we utilized the diffusion-advection equation, where the dispersion and velocity towards x and y are fuzzy parameters. The experts affirm that the pheromone is an important variable concerning trail reoccupation because it influences leaf-cutting ants dispersion and velocity of displacement. The numerical simulations took into account the pheromone through the Fuzzy Rule-Based System (FRBS). The numerical results are compatible with the biological phenomenon studied.

fuzzy parameters; partial differential equations; leaf-cutting ants