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Nelin. Dinam., 2012, Volume 8, Number 3, Pages 473–482 (Mi nd336)  

This article is cited in 4 scientific papers (total in 4 papers)

Coupled universal maps demonstrating Neimark–Saker bifurcation

Alexander 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 examine the dynamics of the coupled system consisting of subsystems, demonstrating the Neimark–Sacker bifurcation. The study of coupled maps on the plane of the parameters responsible for such bifurcation in the individual subsystems is realized. On the plane of parameters characterizing the rotation numbers of the individual subsystems we reveal the complex structures consisting of the quasi-periodic modes of different dimensions and the exact periodic resonances of different orders.

Keywords: maps, bifurcations, phenomena of quasiperiodicity

Full text: PDF file (714 kB)
References: PDF file   HTML file
UDC: 517.9
MSC: 37G35
Received: 27.02.2012
Revised: 16.04.2012

Citation: Alexander P. Kuznetsov, Mikhail V. Pozdnyakov, Julia V. Sedova, “Coupled universal maps demonstrating Neimark–Saker bifurcation”, Nelin. Dinam., 8:3 (2012), 473–482

Citation in format AMSBIB
\Bibitem{KuzPozSed12}
\by Alexander~P.~Kuznetsov, Mikhail~V.~Pozdnyakov, Julia~V.~Sedova
\paper Coupled universal maps demonstrating Neimark--Saker bifurcation
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 3
\pages 473--482
\mathnet{http://mi.mathnet.ru/nd336}


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    This publication is cited in the following articles:
    1. A. P. Kuznetsov, L. V. Tyuryukina, N. Yu. Chernyshov, “Sinkhronizatsiya i kvaziperiodicheskie kolebaniya trekh reaktivno svyazannykh ostsillyatorov”, Nelineinaya dinam., 9:1 (2013), 11–25  mathnet
    2. I. S. Dementeva, A. P. Kuznetsov, A. V. Savin, Yu. V. Sedova, “Kvaziperiodicheskaya dinamika trekh svyazannykh logisticheskikh otobrazhenii”, Nelineinaya dinam., 10:2 (2014), 139–148  mathnet
    3. M. P. Kulakov, G. P. Neverova, E. Ya. Frisman, “Multistabilnost v modelyakh dinamiki migratsionno-svyazannykh populyatsii s vozrastnoi strukturoi”, Nelineinaya dinam., 10:4 (2014), 407–425  mathnet
    4. A. P. Kuznetsov, Yu. V. Sedova, “The simplest map with three-frequency quasi-periodicity and quasi-periodic bifurcations”, Int. J. Bifurcation Chaos, 26:8 (2016), 1630019  crossref  isi
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