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Title: Richness of the dynamics at a Shilnikov bifurcation
Author: Tellols Asensi, Oriol
Director/Tutor: Vieiro Yanes, Arturo
Keywords: Fluxos (Sistemes dinàmics diferenciables)
Treballs de fi de grau
Sistemes dinàmics diferenciables
Sistemes dinàmics hiperbòlics
Teoria de la bifurcació
Flows (Differentiable dynamical systems)
Bachelor's theses
Differentiable dynamical systems
Hyperbolic dynamical systems
Bifurcation theory
Issue Date: 20-Jun-2021
Abstract: [en] In this work, we study the dynamics exhibited in 3 − dimensional parametric continuous dynamical systems containing a homoclinic orbit to a saddle-focus equilibrium. This setting gives rise to the Shilnikov bifurcation, which can be studied using an appropriate Poincaré section that reduces the original system into a discrete 2 − dimensional one. The bifurcation presents various cases, each showing rich and different dynamics. The Shilnikov Theorem describes one of the possible scenarios. This case follows from a careful analysis of a suitable return map that shows that dynamics in some regions is equivalent to the one of the horseshoe map. To illustrate properties and scenarios appearing at the bifurcation, we derive a family of systems with the desired properties and investigate them numerically.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Arturo Vieiro Yanes
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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