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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 7, Pages 1248–1260 (Mi zvmmf9602)  

This article is cited in 7 scientific papers (total in 7 papers)

Multidimensional dynamic processes studied by symbolic analysis in velocity-curvature space

A. V. Makarenko

Constructive Cybernetics Research Group, P.O. 560, Moscow, 101000 Russia

Abstract: A new computer-aided method for the symbolic analysis of discrete mappings and sequences is proposed that is based on a finite discretization of the velocity-curvature space. A minimum alphabet is introduced in a natural way. A number of initial analytical measures are defined that make it possible to study the dynamics structure of multidimensional discrete mappings, continuous systems, and dynamic processes. The proposed analytical method is tested by applying it to a logistic oscillator in the domain to the right of the period-doubling limit point, and the method is shown to be informative. It is revealed that the oscillation structure of the logistic map is highly asymmetric. The critical parameter values are found at which the geometric structure of the map trajectories changes qualitatively.

Key words: symbolic analysis, velocity-curvature space, structure, multidimensional systems, time series, dynamical systems

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:7, 1017–1028

Bibliographic databases:

UDC: 519.62
Received: 17.11.2011
Revised: 20.01.2012

Citation: A. V. Makarenko, “Multidimensional dynamic processes studied by symbolic analysis in velocity-curvature space”, Zh. Vychisl. Mat. Mat. Fiz., 52:7 (2012), 1248–1260; Comput. Math. Math. Phys., 52:7 (2012), 1017–1028

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Makarenko, “Vozmozhnosti simvolicheskogo analiza v prostranstve skorost-krivizna: Tq-bifurkatsii, simmetrii, sinkhronizatsiya”, Nanostruktury. Matematicheskaya fizika i modelirovanie, 2013, no. 3, 21–39  mathscinet  elib
    2. A. V. Makarenko, “Analysis of the time structure of synchronization in multidimensional chaotic systems”, J. Exp. Theor. Phys., 120:5 (2015), 912–921  crossref  isi  elib  scopus
    3. A. V. Makarenko, “Analysis of phase synchronization of chaotic oscillations in terms of symbolic ctq-analysis”, Tech. Phys., 61:2 (2016), 265–273  crossref  isi  elib  scopus
    4. A. V. Makarenko, “Primenenie metodov teorii grafov k issledovaniyu T-sinkhronizatsii khaoticheskikh sistem”, Probl. upravl., 3 (2016), 2–15  mathnet
    5. A. V. Makarenko, “The tq-bifurcation in discrete dynamical systems. General properties”, Proceedings of 2016 International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), ed. V. Tkhai, IEEE, 2016  isi
    6. A. V. Makarenko, “Tq-bifurcations in discrete dynamical systems: Analysis of qualitative rearrangements of the oscillation mode”, J. Exp. Theor. Phys., 123:4 (2016), 666–676  crossref  isi  elib  scopus
    7. A. V. Makarenko, “Metrization of the T-alphabet: measuring the distance between multidimensional real discrete sequences”, Autom. Remote Control, 80:1 (2019), 138–149  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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