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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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Period doubling maps with driving parameter modulated by delayed feedback

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

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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