Dispersión de insectos
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En el siguiente trabajo se deduce un modelo para estudiar la dinámica espacio-temporal de una población considerándola como un proceso de difusión, el enfoque a considerar es una consecuencia del modelo de camino aleatorio, luego se resuelve el modelo básico en forma analítica en una y dos dimensiones, considerando inicialmente el coeficiente de difusión constante y luego considerándolo dependiente de la densidad de población. Se consideran y resuelven en forma analítica las siguientes variaciones del modelo de difusión, el crecimiento exponencial a partir de la natalidad y la mortalidad, el crecimiento logístico a partir de la competencia entre individuos de la misma población y la advección a partir del transporte. Como tal el modelo matemático está determinado por una ecuación diferencial parcial parabólica no lineal, la cual se resuelve en forma exacta utilizando el método autosimilaridad de Bolzmann. Se realizan simulaciones numéricas a partir del esquema de diferencias divididas y del método explicito de Euler, para los diferentes escenarios y como caso de estudio particular se considera la dispersión de la abeja africanizada en Suramérica desde su introducción en Brasil, realizando simulaciones numéricas a partir del método de elementos finitos.
Abstract. In this paper follows a model to study the spatiotemporal dynamics of a population regarding it as a difusion process, the approach to consider is a consequence of the random walk model, then the basic model is solved analytically in one and two dimensions initially considering the difusion coe¢ cient constant and then considering dependent density. Are considered and solved analytically in the following variations in the di¤usion model, the exponential growth from birth and mortality, logistic growth from competition between individuals of the same population and advection from transportation. As such, the mathematical model is determined by a parabolic partial difeerential equation nonlinear, which is resolved accurately using the self-similaritythe of Bolzmann method. Numerical simulations are performed from the divided diference scheme and explicit Euler method for di¤erent scenarios and as a particular case study considered the dispersion of the Africanized bee in South America since its introduction in Brazil, performing numerical simulations from finite elements method.
Abstract. In this paper follows a model to study the spatiotemporal dynamics of a population regarding it as a difusion process, the approach to consider is a consequence of the random walk model, then the basic model is solved analytically in one and two dimensions initially considering the difusion coe¢ cient constant and then considering dependent density. Are considered and solved analytically in the following variations in the di¤usion model, the exponential growth from birth and mortality, logistic growth from competition between individuals of the same population and advection from transportation. As such, the mathematical model is determined by a parabolic partial difeerential equation nonlinear, which is resolved accurately using the self-similaritythe of Bolzmann method. Numerical simulations are performed from the divided diference scheme and explicit Euler method for di¤erent scenarios and as a particular case study considered the dispersion of the Africanized bee in South America since its introduction in Brazil, performing numerical simulations from finite elements method.