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JOURNALS // Russian Journal of Nonlinear Dynamics // Archive

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

This article is cited in 4 papers

Coupled universal maps demonstrating Neimark–Saker bifurcation

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

a Kotel’nikov’s 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.

UDC: 517.9

MSC: 37G35

Received: 27.02.2012
Revised: 16.04.2012



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