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http://hdl.handle.net/2445/185699
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 |
URI: | http://hdl.handle.net/2445/185699 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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tfg_tellols_asensi_oriol.pdf | Memòria | 3.91 MB | Adobe PDF | View/Open |
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