Haro, ÀlexMatías Vejer, Sara2016-01-272016-01-272015-06-30https://hdl.handle.net/2445/69026Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2015, Director: Àlex HaroThe 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.64 p.application/pdfcatcc-by-nc-nd (c) Sara Matías Vejer, 2015http://creativecommons.org/licenses/by-nc-nd/3.0/esOnesTreballs de fi de grauCamps vectorialsEquacions de reacció-difusióExponents de LyapunovSolucions (Química)WavesBachelor's thesesVector fieldsLyapunov exponentsSolution (Chemistry)Reaction-diffusion equationsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess