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

For citation:

Kuznetsov A. P., Kuznetsova A. Y., Sataev I. R. Critical behavior оf thе мар with Neimark-Sackers bifurcation for the phase synchronization breakup at the accumulation point of period doubling cascade. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 1, pp. 12-18. DOI: 10.18500/0869-6632-2003-11-1-12-18

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2003-11-1-12-18

Critical behavior оf thе мар with Neimark-Sackers bifurcation for the phase synchronization breakup at the accumulation point of period doubling cascade

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuznetsova Anna Yurevna, Saratov State University
Sataev Igor Rustamovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

Universality and scaling are discussed for the case of the phase synchronization breakup at the accumulation point of period doubling cascade in two-dimensional map with supercritical Neimark-Sackers bifurcation.

Key words: 
-
Acknowledgments: 
This work was supported by the Federal Target Programme Integration and the American Foundation for Civic Research and Development (CRDF grant REC-006), as well by the Foundation for Promotion of National Science
Reference: 
  1. Schuster HG. Deterministic Chaos: An Introduction. VCH Publishers; 1984. 220 p.
  2. Kuznetsov SP. Dynamic Chaos. Moscow: Fizmatlit; 2001. 296 p. (in Russian).
  3. Thompson JM, Stewart HB. Nonlinear Dynamics and Chaos. Wiley and Sons; New York, 1986. 392 p.
  4. Kuznetsov SP, Sataev IR. Period-doubling for two-dimensional non-invertible maps: Renormalization group analysis and quantitative universality. Physica D. 1997;101(3–4):249–269. DOI: 10.1016/S0167-2789(96)00237-0.
  5. Kuznetsov SP, Sataev IR. New types оf critical dynamics for two-dimensional maps. Phys. Lett. А. 1992;162(3):236–242. DOI: 10.1016/0375-9601(92)90440-W.
  6. Kuznetsov AP, Kuznetsov SP, Sataev IR. A variety of period-doubling universality classes in multi-parameter analysis оf transition to chaos. Physica D. 1997;109(1–2):91–112. DOI: 10.1016/S0167-2789(97)00162-0.
  7. Maistrenko V, Maistrenko Y, Sushko I. Noninvertible two-dimensional maps arising in radiophysics. Int. J. Bifurc. Chaos. 1994;4(2):383–400. DOI: 10.1142/S0218127494000253.
Received: 
21.10.2002
Accepted: 
12.05.2003
Available online: 
10.11.2023
Published: 
30.05.2003
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