TITLE:
A Model of Cellular Automata for the Fuzzy Control of Aphids
AUTHORS:
Magda da Silva Peixoto, Laécio Carvalho de Barros, Rodney Carlos Bassanezi
KEYWORDS:
Fuzzy Sets, Fuzzy Rule Base, Cellular Automata, Simulations, Pesticides
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.8,
May
5,
2014
ABSTRACT: 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.