Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems |
Autor: | Roulet, J.; Mindlin, G.B. |
Filiación: | Physics Department, Princeton University, Princeton, NJ 08544, United States Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, C1053ABJ, Argentina IFIBA, CONICET, Ciudad Universitaria, Buenos Aires, 1428, Argentina
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Palabras clave: | 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) |
Año: | 2017
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Volumen: | 27
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Número: | 13
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DOI: |
http://dx.doi.org/10.1142/S0218127417300452 |
Título revista: | International Journal of Bifurcation and Chaos
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Título revista abreviado: | Int. J. Bifurcation Chaos
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ISSN: | 02181274
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v27_n13_p_Roulet |
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Citas:
---------- APA ----------
Roulet, J. & Mindlin, G.B.
(2017)
. A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems. International Journal of Bifurcation and Chaos, 27(13).
http://dx.doi.org/10.1142/S0218127417300452---------- CHICAGO ----------
Roulet, J., Mindlin, G.B.
"A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems"
. International Journal of Bifurcation and Chaos 27, no. 13
(2017).
http://dx.doi.org/10.1142/S0218127417300452---------- MLA ----------
Roulet, J., Mindlin, G.B.
"A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems"
. International Journal of Bifurcation and Chaos, vol. 27, no. 13, 2017.
http://dx.doi.org/10.1142/S0218127417300452---------- VANCOUVER ----------
Roulet, J., Mindlin, G.B. A Diagrammatic Representation of Phase Portraits and Bifurcation Diagrams of Two-Dimensional Dynamical Systems. Int. J. Bifurcation Chaos. 2017;27(13).
http://dx.doi.org/10.1142/S0218127417300452