Applied Mathematics > Vol.5 No.8, May 2014

Magda da Silva Peixoto, Laécio Carvalho de Barros, Rodney Carlos Bassanezi

Departamento de Física, Química e Matemática, Universidade Federal de S?o Carlos, Sorocaba, Brazil.
Departamento de Matemática Aplicada, IMECC, Universidade Estadual de Campinas, Campinas, Brazil.

Pesticides are substances used to prevent, destroy or mitigate any pest. We have adopted in this paper the Cellular Automata model to study the dispersion of the aphids in the block of citric trees using the pesticides (chemical control) and the biological agent (biological control). The main purpose of this research is the development of a simple and specific methodology to study Citrus Sudden Death (CSD). CSD is a disease that has affected sweet orange trees grafted on Rangpur lime in the state of S?o Paulo-Brazil. Some studies suggest that this disease has been caused by a virus and it is transmitted by insects known as aphids (vector). The ladybug was selected among the most known enemies of aphids in citrus in Brazil. In order to elaborate a predator-prey type of model to study the interaction between aphids (preys) and ladybugs (predators) in citriculture we have used a fuzzy rule-based system (FRBS). The states of the variables of the system (inputs) are the density of preys and the density of predators and their variations are the outputs. Therefore we take into account the effect of the wind in the space covered by the aphid, since the wind is important for the flight of the aphid as described in Peixoto et al. (2008) [1]. After, we used a FRBS to establish the relationship between the quantity of pesticides and the density of the preys. The simulations have been performed and have been compared between blocks with the presence of both aphids and ladybugs without the use of pesticides and the presence of them with the use of these ones using the Cellular Automata model. Numerical simulations allow us to foresee the behavior of the system, hence creating a spectrum of possibilities and proposing control techniques for different initial scenarios.

Fuzzy Sets, Fuzzy Rule Base, Cellular Automata, Simulations, Pesticides

Peixoto, M. , Barros, L. and Bassanezi, R. (2014) A Model of Cellular Automata for the Fuzzy Control of Aphids. Applied Mathematics, 5, 1133-1141. doi: 10.4236/am.2014.58106.