Um modelo de equações a diferenças integrais para o crescimento e propagação do arroz branco e arroz vermelho (Oryza sativa L.)

Abstract

The main objective of this work is to analyze the growth and propagation dynamics of white rice Oryza sativa l. and the red rice Oryza sativa l., through a model composed of integral difference equations, discrete in time and continuous in space. We chose this model because it describes well the temporal evolution of annual plants with seed banks and that disperse their seeds at distances close to the plant that produced them. The values ​​for the parameters present in the model were obtained in the literature, in order to analyze the differences in growth and propagation between the two types of rice. Red rice is a weed, if we consider that the objective of the producers is the cultivation of white rice. The adopted model considers intraspecific competition (density dependence) among plants for water, light and nutrients. Thus, we performed numerical simulations to verify how the variation in density dependence alters the productivity and quantity of adult plants per cycle, for both types of rice. This was verified through the amount of seeds and adult plants generated from an initial amount, per meter of cultivated land. In addition, red rice (pest) propagates faster, so its survival is longer, due to the dormancy process that can last up to 12 years. Finally, after using the Mathematica program, we concluded that the numerical simulations were indispensable for the analysis of the results, since the adopted model cannot be analyzed analytically and the parameter values ​​for both types of rice are very similar.