A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems

We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that discard their quantitative information. All codimension 1 bifu...

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Detalles Bibliográficos
Publicado: 2017
Materias:
Bifurcations
Nonlinear dynamics
Two-dimensional systems
Dynamical systems
Dynamics
Graphic methods
Bifurcation diagram
Codimension-1 bifurcations
Diagrammatic representations
Partial information
Qualitative features
Quantitative information
Topological features
Bifurcation (mathematics)
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v27_n13_p_Roulet
http://hdl.handle.net/20.500.12110/paper_02181274_v27_n13_p_Roulet
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02181274_v27_n13_p_Roulet
record_format dspace
spelling paper:paper_02181274_v27_n13_p_Roulet2023-06-08T15:21:20Z A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems Bifurcations Nonlinear dynamics Two-dimensional systems Dynamical systems Dynamics Graphic methods Bifurcation diagram Codimension-1 bifurcations Diagrammatic representations Partial information Qualitative features Quantitative information Topological features Two-dimensional systems Bifurcation (mathematics) We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that discard their quantitative information. All codimension 1 bifurcations are naturally embodied in the possible ways of transitioning smoothly between diagrams. We introduce a representation of bifurcation curves in parameter space that guides the proposition of bifurcation diagrams compatible with partial information about the system. © 2017 World Scientific Publishing Company. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v27_n13_p_Roulet http://hdl.handle.net/20.500.12110/paper_02181274_v27_n13_p_Roulet
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Bifurcations
Nonlinear dynamics
Two-dimensional systems
Dynamical systems
Dynamics
Graphic methods
Bifurcation diagram
Codimension-1 bifurcations
Diagrammatic representations
Partial information
Qualitative features
Quantitative information
Topological features
Two-dimensional systems
Bifurcation (mathematics)
spellingShingle Bifurcations
Nonlinear dynamics
Two-dimensional systems
Dynamical systems
Dynamics
Graphic methods
Bifurcation diagram
Codimension-1 bifurcations
Diagrammatic representations
Partial information
Qualitative features
Quantitative information
Topological features
Two-dimensional systems
Bifurcation (mathematics)
A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems
topic_facet Bifurcations
Nonlinear dynamics
Two-dimensional systems
Dynamical systems
Dynamics
Graphic methods
Bifurcation diagram
Codimension-1 bifurcations
Diagrammatic representations
Partial information
Qualitative features
Quantitative information
Topological features
Two-dimensional systems
Bifurcation (mathematics)
description We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that discard their quantitative information. All codimension 1 bifurcations are naturally embodied in the possible ways of transitioning smoothly between diagrams. We introduce a representation of bifurcation curves in parameter space that guides the proposition of bifurcation diagrams compatible with partial information about the system. © 2017 World Scientific Publishing Company.
title A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems
title_short A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems
title_full A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems
title_fullStr A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems
title_full_unstemmed A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems
title_sort diagrammatic representation of phase portraits and bifurcation diagrams of two-dimensional dynamical systems
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v27_n13_p_Roulet
http://hdl.handle.net/20.500.12110/paper_02181274_v27_n13_p_Roulet
_version_ 1768545047827972096

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