Abstract:
The work is devoted to the exposition of the method of localizing the Arnold tongues for finite-dimensional dynamical systems with a discrete time which are the sets corresponding to rationally synchronized relations between the system's parameters. Such sets correspond to regions of parameter values for which the system has cycles of certain periods. The method allows us to obtain an approximate representation of the Arnold tongues, to study their properties in the major and minor resonances.
Keywords:
bifurcation, dynamical systems, Arnold tongues, operator equations, functionalization of parameter.
\Bibitem{Yum13}
\by M.~G.~Yumagulov
\paper Localization of Arnold tongues of discrete dynamical systems
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 2
\pages 109--130
\mathnet{http://mi.mathnet.ru/eng/ufa202}
\crossref{https://doi.org/10.13108/2013-5-2-109}
\elib{https://elibrary.ru/item.asp?id=19063040}
Linking options:
https://www.mathnet.ru/eng/ufa202
https://doi.org/10.13108/2013-5-2-109
https://www.mathnet.ru/eng/ufa/v5/i2/p109
This publication is cited in the following 5 articles:
M. G. Yumagulov, M. F. Fazlytdinov, “Bifurcation formulas and algorithms of constructing central manifolds of discrete dynamical systems”, Russian Math. (Iz. VUZ), 63:3 (2019), 62–77
N. I. Gusarova, S. A. Murtazina, M. F. Fazlytdinov, M. G. Yumagulov, “Operator methods for calculating Lyapunov values in problems on local bifurcations of dynamical systems”, Ufa Math. J., 10:1 (2018), 25–48
M. G. Yumagulov, O. N. Belikova, N. R. Isanbaeva, “Bifurcation near boundaries of regions of stability of libration points in the three-body problem”, Astron. Rep., 62:2 (2018), 144–153
M. G. Yumagulov, I. Zh. Mustafina, L. S. Ibragimova, “A study of the boundaries of stability regions in two-parameter dynamical systems”, Autom. Remote Control, 78:10 (2017), 1790–1802
M. F. Fazlytdinov, M. G. Yumagulov, “Priznaki ustoichivosti tsiklov v zadache o yazykakh Arnolda”, Matematicheskoe i programmnoe obespechenie sistem v promyshlennoi i sotsialnoi sferakh, 2014, no. 2 (5), 19–23
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