Vieiro Yanes, ArturoTellols Asensi, Oriol2022-05-182022-05-182021-06-20https://hdl.handle.net/2445/185699Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Arturo Vieiro Yanes[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.77 p.application/pdfengcc-by-nc-nd (c) Oriol Tellols Asensi, 2021http://creativecommons.org/licenses/by-nc-nd/3.0/es/Fluxos (Sistemes dinàmics diferenciables)Treballs de fi de grauSistemes dinàmics diferenciablesSistemes dinàmics hiperbòlicsTeoria de la bifurcacióFlows (Differentiable dynamical systems)Bachelor's thesesDifferentiable dynamical systemsHyperbolic dynamical systemsBifurcation theoryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess