Sistemas diferenciales lineales a trozos: Ciclos límite y análisis de bifurcaciones

Tesis descargada desde TESEO

Detalles Bibliográficos
Autor: Vela Felardo, Elisabet
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2013
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/55165
Acceso en línea:http://hdl.handle.net/11441/55165
Access Level:acceso abierto
Palabra clave:Matemáticas
Análisis y análisis funcional
Ecuaciones diferenciales ordinarias
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dc.title.none.fl_str_mv Sistemas diferenciales lineales a trozos: Ciclos límite y análisis de bifurcaciones
title Sistemas diferenciales lineales a trozos: Ciclos límite y análisis de bifurcaciones
spellingShingle Sistemas diferenciales lineales a trozos: Ciclos límite y análisis de bifurcaciones
Vela Felardo, Elisabet
Matemáticas
Análisis y análisis funcional
Ecuaciones diferenciales ordinarias
title_short Sistemas diferenciales lineales a trozos: Ciclos límite y análisis de bifurcaciones
title_full Sistemas diferenciales lineales a trozos: Ciclos límite y análisis de bifurcaciones
title_fullStr Sistemas diferenciales lineales a trozos: Ciclos límite y análisis de bifurcaciones
title_full_unstemmed Sistemas diferenciales lineales a trozos: Ciclos límite y análisis de bifurcaciones
title_sort Sistemas diferenciales lineales a trozos: Ciclos límite y análisis de bifurcaciones
dc.creator.none.fl_str_mv Vela Felardo, Elisabet
author Vela Felardo, Elisabet
author_facet Vela Felardo, Elisabet
author_role author
dc.contributor.none.fl_str_mv Ponce Núñez, Enrique
Ros Padilla, Francisco Javier
Matemática Aplicada II
TIC130: Investigacion en Sistemas Dinamicos en Ingenieria
dc.subject.none.fl_str_mv Matemáticas
Análisis y análisis funcional
Ecuaciones diferenciales ordinarias
topic Matemáticas
Análisis y análisis funcional
Ecuaciones diferenciales ordinarias
description Tesis descargada desde TESEO
publishDate 2013
dc.date.none.fl_str_mv 2013
dc.type.none.fl_str_mv info:eu-repo/semantics/doctoralThesis
info:eu-repo/semantics/publishedVersion
format doctoralThesis
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/55165
url http://hdl.handle.net/11441/55165
dc.language.none.fl_str_mv Español
language_invalid_str_mv Español
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
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spelling Sistemas diferenciales lineales a trozos: Ciclos límite y análisis de bifurcacionesVela Felardo, ElisabetMatemáticasAnálisis y análisis funcionalEcuaciones diferenciales ordinariasTesis descargada desde TESEOThe class of piecewise-linear differential systems (PWL systems, for short) is an important class of nonlinear dynamical systems. They naturally appear in realistic nonlinear engineering models, and are used in mathematical biology as well, where they constitute approximate models. Therefore, they constitute a significant subclass of piecewise-smooth dynamical systems. From the family of planar, continuous PWL systems (CPWL2, for short) we study systems with only two zones (2CPWL2 systems), and systems with three zones with or without symmetry with respect to the origin (S3CPWL2 systems). Some discontinuous PWL systems with only two zones (2DPWL2, for short) and symmetric PWL systems in dimension 3, namely S3CPWL3, are also considered. After an introduction, in Chapter 2 we review some terminology and results related to canonical forms in the study of PWL systems along with certain techniques that are useful for the bifurcation analysis of their periodic orbits. We review general results in dimension n, but we later deal only with systems in dimension 2 and 3. Next, Chapter 3 is completely devoted to planar PWL systems. Some boundary equilibrium bifurcations (BEB, for short) are characterized, putting emphasis in the ones capable of giving rise to limit cycles. We exploit and extend some recent results, which allows us to pave the way for a shorter proof of Lum-Chua conjecture. After other general results for existence and uniqueness of limit cycles in 3CPWL2 systems, we show some applications of the theory in nonlinear electronics. In a different direction of research, it is introduced a new family of algebraically computable piecewise linear nodal oscillators and shown some real electronic devices that belong to the family. The outstanding feature of this family makes it an exceptional benchmark for testing approximate methods of analysis of oscillators. Finally, we include our only contribution in the exciting world of discontinuous PWL systems: the analysis of the focus-center-limit cycle bifurcation in planar PWL systems with two zones and without a proper sliding set, which naturally includes the continuous case. Chapter 4 represents our particular incursion in PWL systems in dimension 3, namely in S3CPWL3 ones, notwithstanding some results are also interesting for 2CPWL3 vector fields. Pursuing the aim of fill in the pending gaps in the catalog of possible bifurcations, we study some unfoldings of the analogous to Hopf-pitchfork bifurcations in PWL systems. Our theorems predict the simultaneous bifurcation of 3 limit cycles but we also formulate a natural, strongly numerically based conjecture on the simultaneous bifurcation of 5 limit cycles. Finally, in Chapter 5 some conclusions and recommendations for future work are offered for consideration of interested readers. For the sake of concision, we want to specifically mention the main mathematical contributions included in this thesis. ¿ A new approach, following Massera¿s method, to get a concise proof for the Lum-Chua Conjecture in planar PWL systems with two zones (2CPWL2). ¿ Characterization for a variety of boundary equilibrium bifurcations (BEB¿s, for short) in 2CPWL2 systems. ¿ Alternative proofs of existence and uniqueness results for limit cycles in an important family of planar PWL systems with three zones (3CPWL2). ¿ Characterization for a variety of boundary equilibrium bifurcations (BEB¿s, for short) in 3CPWL2 systems, detecting some situations with two nested limit cycles surrounding the only equilibrium point. ¿ Analysis of the focus-center-limit cycle bifurcation in discontinuous planar PWL systems without sliding set. ¿ A thorough analysis of electronic Wien bridge oscillators, characterizing qualitatively (and quantitatively in some cases) the oscillatory behaviour and determining the parameter regions for oscillations. ¿ Analysis of a new family of algebraically computable nodal oscillators, including real examples of members of the family. ¿ Analysis of some specific unfolding for the Hopf-zero or Hopf-pitchfork bifurcation and its main degenerations in symmetric PWL systems in 3D (S3CPWL3), with the detection of the simultaneous bifurcation of three limit cycles. ¿ Study of some real electronic devices where the Hopf-zero bifurcation appears.Ponce Núñez, EnriqueRos Padilla, Francisco JavierMatemática Aplicada IITIC130: Investigacion en Sistemas Dinamicos en Ingenieria2013info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/55165reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)Españolinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/551652026-06-17T12:51:07Z
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