ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Kuznetsov A. P., Novikov E. V., Savin A. V. Period doubling maps with driving parameter modulated by delayed feedback. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 4, pp. 33-48. DOI: 10.18500/0869-6632-2008-16-4-33-64

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Russian
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Article
UDC: 
517.9

Period doubling maps with driving parameter modulated by delayed feedback

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Novikov Evgenij Vjacheslavovich, Saratov State University
Savin Aleksej Vladimirovich, Saratov State University
Abstract: 

It was shown that addition of modulation of driving parameter with using delay can be considered as physically reasoned method of construction two-dimensional maps with nonfixed Jacobian. The examples of such two-parameter and three-parameter maps were presented. The conditions of Neumark–Sacker’s bifurcation, period doubling and resonance 1:2 were obtained. The structure of parameter space was studied by dynamical regimes maps method and the regions of quasiperiodic regimes and different synchronous regimes were revealed.

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Received: 
29.12.2007
Accepted: 
19.06.2008
Published: 
31.10.2008
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