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tfg_tellols_asensi_oriol.pdf (3.81 MB)

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Bachelor thesis

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2021-06-20

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cc-by-nc-nd (c) Oriol Tellols Asensi, 2021
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/185699

Richness of the dynamics at a Shilnikov bifurcation

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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.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Arturo Vieiro Yanes

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Fluxos (Sistemes dinàmics diferenciables), Treballs de fi de grau, Sistemes dinàmics diferenciables, Sistemes dinàmics hiperbòlics, Teoria de la bifurcació

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Flows (Differentiable dynamical systems), Bachelor's theses, Differentiable dynamical systems, Hyperbolic dynamical systems, Bifurcation theory

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

TELLOLS ASENSI, Oriol. Richness of the dynamics at a Shilnikov bifurcation. [consulted: 6 of June of 2026]. Available at: https://hdl.handle.net/2445/185699

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