Modelagem e solução numérica de equações reação-difusão em processos biológicos

Abstract

Biological phenomena are all and any event that can be observed in living beings. The study of these phenomena enables us to propose explanations for its mechanisms in order to understand causes and e ects. One can cite as examples of biological phenomena the behavior of cells as respiration, reproduction, metabolism and cell death. Reactiondi usion equations are often used to model biological phenomena. Reaction-di usion systems can produce stable spatial patterns from a uniform initial distribution, this phenomenon is known as Turing instability. This dissertation presents an analysis of the Turing instability as well as numerical results for the solution of three biological models, model Schnakenberg, model of glycolysis and model of blood coagulation. The Schnakenberg model is used to describe an autocatalytic chemical reaction and glycolysis model refers to the process of metabolic breakdown of the glucose molecule to provide energy for cellular metabolism, these two models are frequently reported in the literature. The third model is newer and describes the phenomenon of blood coagulation. The method of lines is used in the numerical solutions, where the spatial discretization is done through a nite di erence scheme. The resulting system of ordinary di erential equations is then solved by an adaptive integration scheme with the use of the package for scienti c computing of Python language, Scipy.