Fuzzy modeling of reoccupation of a leaf-cutting ants’ trail

Rosana Sueli da Motta Jafelice, César Guilherme Almeida


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 to-
wards 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 numer-
ical results are compatible with the biological phenomenon studied.

Full Text:



R.S. Cantrell, C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, John Wiley and Sons Ltd., England, 2003.

M. Dorigo, T. Stützle, Ant Colony Optimization, Massachusetts Institute of Tecnology, USA, 2004.

R.M. Jafelice, C.G. Almeida, J.F.C.A. Meyer, H.L. Vasconcelos, Dispersal of

Leaf-Cutting Ants: Fuzzy Mathematical Modeling, Numerical Approximation

and Simulations. In: IFSA Word Congress - EUSFLAT Conference, Lisboa,

, pp. 271-276.

R.M. Jafelice, C.G. Almeida, J.F.C.A. Meyer, H.L. Vasconcelos, A Fuzzy-

parameter Dispersion-attraction Partial Differential Model for an Ant Colony.

In: XXXII Congresso Nacional de Matemática Aplicada e Computacional,

Cuiabá, 2009, pp. 87-93.

R.M. Jafelice, C.G. Almeida, J.F.C.A. Meyer, H.L. Vasconcelos, Fuzzy pa-

rameters in a partial differential equation model for population dispersal of

leaf-cutting ants. Nonlinear Analysis: Real World Applications, 12 (2011)


H. Kardestuncer, D.H. Norrie, Finite Elements Handbook, McGraw-Hill, New

York, 1987.

H.L. Vasconcelos, Foraging activity of two species of leaf-cutting ants (Atta) in a primary forest of the central Amazon, Insectes Sociaux 37 (2) (1990) 131-145.

DOI: https://doi.org/10.5540/tema.2015.016.01.0041

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


Indexed in:



Desenvolvido por:

Logomarca da Lepidus Tecnologia