A Model of Cellular Automata for the Fuzzy Control of Aphids

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.

DOI: 10.4236/am.2014.58106                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Peixoto, M.S., Barros, L.C. and Bassanezi, R.C. (2008) A Model of Cellular Automata for the Spatial and Temporal Analysis of Citrus Sudden Death with the Fuzzy Parameter. Ecological Modelling, 214, 45-52. http://dx.doi.org/10.1016/j.ecolmodel.2008.01.018
[2]	Bassanezi, R.B., Bergamin Filho, A., Amorim, L., Gimenes-Fernandes, N. and Gottwald, T.R. (2003) Spatial and Temporal Analysis of Citrus Sudden Death as a Tool to Generate Hypothesis Its Etiology. Phytopathology, 93, 502-512. http://dx.doi.org/10.1094/PHYTO.2003.93.4.502
[3]	Wolfram, S. (1994) Cellular Automata and Complexity. Addison-Wesley Publishing Company, Massachusetts.
[4]	Ermentrout, G.B. and Edelstein-Keshet, L. (1993) Cellular Automata Approaches to Biological Modeling. Journal of Theoretical Biology, 160, 97-133. http://dx.doi.org/10.1006/jtbi.1993.1007
[5]	Breckling, B., Muller, F., Reuter, H., Holker, F. and Franzle, O. (2005) Emergent Properties in Individual-Based Ecological Models—Introducing Case Studies in a Ecosystem Research Context. Ecological Modelling, 186, 376-388. http://dx.doi.org/10.1016/j.ecolmodel.2005.02.008
[6]	Zadeh, L.A. (1965) Fuzzy Sets. Informat. Control, 8, 338-353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
[7]	Jafelice, R.M., Barros, L.B., Bassanezi, R.C. and Gomide, F. (2003) Fuzzy Modeling Symptomatic HIV Virus Infected Population. Bulletin of Mathematical Biology, 66, 1597-1620. http://dx.doi.org/10.1016/j.bulm.2004.03.002
[8]	Klir, G.J. and Yuan, B. (1995) Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, New Jersey.
[9]	Pedrycs, W. and Gomide, F. (1998) An Introduction to Fuzzy Sets: Analysis and Design. Massachusets Institute of Technology, Cambridge.
[10]	Edelstein-Keshet, L. (1987) Mathematical Models in Biology. McGraw-Hill, Inc., New York.