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Nelin. Dinam., 2012, Volume 8, Number 3, Pages 461–471 (Mi nd335)  

This article is cited in 5 scientific papers (total in 5 papers)

Universal two-dimensional map and its radiophysical realization

Alexander P. Kuznetsova, Sergey P. Kuznetsova, Mikhail V. Pozdnyakovb, Julia V. Sedovaa

a Kotelnikovs Institute of Radio-Engineering and Electronics of RAS, Saratov Branch Zelenaya 38, Saratov, 410019 Russia
b Saratov State Technical University Polytechnicheskaya 77, Saratov, 410054, Russia

Abstract: We suggest a simple two-dimensional map, parameters of which are the trace and Jacobian of the perturbation matrix of the fixed point. On the parameters plane it demonstrates the main universal bifurcation scenarios: the threshold to chaos via period-doublings, the situation of quasiperiodic oscillations and Arnold tongues. We demonstrate the possibility of implementation of such map in radiophysical device.

Keywords: maps, bifurcations, phenomena of quasiperiodicity

Full text: PDF file (637 kB)
References: PDF file   HTML file
UDC: 517.9
MSC: 37G35
Received: 27.02.2012
Revised: 16.04.2012

Citation: Alexander P. Kuznetsov, Sergey P. Kuznetsov, Mikhail V. Pozdnyakov, Julia V. Sedova, “Universal two-dimensional map and its radiophysical realization”, Nelin. Dinam., 8:3 (2012), 461–471

Citation in format AMSBIB
\Bibitem{KuzKuzPoz12}
\by Alexander~P.~Kuznetsov, Sergey~P.~Kuznetsov, Mikhail~V.~Pozdnyakov, Julia~V.~Sedova
\paper Universal two-dimensional map and its radiophysical realization
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 3
\pages 461--471
\mathnet{http://mi.mathnet.ru/nd335}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. P. Kuznetsov, M. V. Pozdnyakov, Yu. V. Sedova, “Svyazannye universalnye otobrazheniya s bifurkatsiei Neimarka–Sakera”, Nelineinaya dinam., 8:3 (2012), 473–482  mathnet
    2. G. P. Neverova, E. Ya. Frisman, “Matematicheskoe modelirovanie dinamiki lokalnykh odnorodnykh populyatsii s uchetom effektov zapazdyvaniya”, Matem. biologiya i bioinform., 10:2 (2015), 309–324  mathnet  crossref
    3. O. L. Revutskaya, G. P. Neverova, M. P. Kulakov, E. Ya. Frisman, “Model dinamiki chislennosti dvukhvozrastnoi populyatsii: ustoichivost, multistabilnost i khaos”, Nelineinaya dinam., 12:4 (2016), 591–603  mathnet  crossref  elib
    4. Neverova G.P., Zhdanova O.L., Ghosh B., Frisman E.Ya., “Dynamics of a Discrete-Time Stage-Structured Predator-Prey System With Holling Type II Response Function”, Nonlinear Dyn., 98:1 (2019), 427–446  crossref  zmath  isi  scopus
    5. S. D. Glyzin, S. A. Kaschenko, “Semeistvo konechnomernykh otobrazhenii, indutsirovannykh logisticheskim uravneniem s zapazdyvaniem”, Matem. modelirovanie, 32:3 (2020), 19–46  mathnet  crossref
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