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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
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
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
Volumen:27
Número:13
DOI: http://dx.doi.org/10.1142/S0218127417300452
Título revista:International Journal of Bifurcation and Chaos
Título revista abreviado:Int. J. Bifurcation Chaos
ISSN:02181274
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