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

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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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Autores principales: Roulet, J., Mindlin, G.B.
Formato: JOUR
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: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 todo:paper_02181274_v27_n13_p_Roulet
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spelling todo:paper_02181274_v27_n13_p_Roulet2023-10-03T15:10:45Z A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems Roulet, J. Mindlin, G.B. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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)
Roulet, J.
Mindlin, G.B.
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.
format JOUR
author Roulet, J.
Mindlin, G.B.
author_facet Roulet, J.
Mindlin, G.B.
author_sort Roulet, J.
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
url http://hdl.handle.net/20.500.12110/paper_02181274_v27_n13_p_Roulet
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AT mindlingb adiagrammaticrepresentationofphaseportraitsandbifurcationdiagramsoftwodimensionaldynamicalsystems
AT rouletj diagrammaticrepresentationofphaseportraitsandbifurcationdiagramsoftwodimensionaldynamicalsystems
AT mindlingb diagrammaticrepresentationofphaseportraitsandbifurcationdiagramsoftwodimensionaldynamicalsystems
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