Dispersal of Leaf-Cutting Ants: fuzzy mathematical modeling, numerical approximation and simulations

The objective of this paper is to propose a model for the occupation, by leaf-cutting ants, of an attractive area using a form of the diffusion-advection partial differential equation, in which the population dispersal is modeled using a fuzzy parameter. In the studied domain there is an attractive region, which can represent areas with an elevated concentration of palatable host-plants with better nutritious qualities. The developed algorithm uses information about the foraging behavior of a leaf-cutting ant colony from the Amazon region, in northern Brazil. The solution of the chosen partial differential equation is approximated using first order finite triangular elements and determines population dispersal with the use of a fuzzy rule-based system, which depends upon the number of individuals in the population and terrain characteristics. The numerical algorithm was developed in a MATLAB environment. The calculated solution is compatible with ant behavior when there is an attraction region nearby, as reported in the literature. Keywords— Fuzzy Set; Leaf-Cutting Ants; Mathematical Modeling; Numerical Methods; Partial Differential Equation;