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Métodos de homogenización y bifurcaciones en modelos sobre dispersión ecológica

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Abstract

Este artculo sobre metodos de la modelamiento para sistemas ecologicos resulto del proyecto de investigacion denominado \Movilizacion Matematica y Sistemas Dinamicos en algunos Ecosistemas\, donde estudiamos el paradigma de los sistemas dinamicospara la descripcion de la dispersion ecologica. Este enfoque ha sido muy exitoso para conocer variedad de fenomenos de las ciencias naturales y sociales; pero debido a las interacciones complejas entre: clima, suelo, agua, biotica, la presencia de la memoria en losprocesos dada por la historia local integrada a un entorno, a la morfo-dinamica moldeada por el ujo de poblaciones, resulta que los ecosistemas son mas complejos y deben ser considerados como un sistema dinamico adaptativo o emergente. En este trabajoescribimos la evolucion de ecosistemas, que se caracterizan por : interdenicion de sus variables a partir de la toma de datos, la estimacion estadstica de los parametros, la existencia de varias escalas espaciotemporales; por ello integramos metodos estadsticoscon los cambios de variables multiescala para homogenizar y promediar sus perturbaciones singulares.Los modelos estudiados se aplican a procesos de migracion dispersivos que incluyen interrelaciones complejas, en donde se consideran el autocontrol resiliente, siempre y cuando las uctuaciones no superen un umbral especco.

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