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Title: Estudi de la dinàmica de models de reacció-difusió
Author: Matías Vejer, Sara
Director/Tutor: Haro, Àlex
Keywords: Ones
Treballs de fi de grau
Camps vectorials
Equacions de reacció-difusió
Exponents de Lyapunov
Solucions (Química)
Bachelor's thesis
Vector fields
Lyapunov exponents
Solution (Chemistry)
Reaction-diffusion equations
Issue Date: 30-Jun-2015
Abstract: The Fisher-KPP equation is a model for invasion processes and the Brusselator is an autocatalytic model used in chemistry. Both of them belong to the reaction-diffusion models family. The purpose of this project is to study the behaviour and dynamics of their solutions. Having made a brief introduction into the weak solutions class to understand the existence and uniqueness of solutions, we focus on the phenomenon of traveling waves and its link with heteroclinic connections in a vector field. The Lyapunov theory provides us with the necessary tools to reach the existence of traveling waves in Fisher-KPP model. To complete the study we analyze the presence of a Hopf bifurcation in the Brusselator model.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2015, Director: Àlex Haro
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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