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

For citation:

Seleznev E. P., Zaharevich A. M. Fractal properties оf synchronous chaos in coupled maps. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 5, pp. 19-24. DOI: 10.18500/0869-6632-2002-10-5-19-24

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon and_2002-5_seleznev_etal.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
530.18
DOI: 
10.18500/0869-6632-2002-10-5-19-24

Fractal properties оf synchronous chaos in coupled maps

Autors: 
Seleznev Evgeny Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Zaharevich Andrej Mihajlovich, Saratov State University
Abstract: 

We investigate numerically the influence of asymmetry оn synchronous chaos in the system of dissipatively coupled quadratic maps. It is shown that the synchronous chaotic attractor becomes fractal after the loss оf transversal superstability in the asymmetrical system. Correlation dimension of the attractor demonstrates nonmonotonic dependence on the coupling coefficient near the synchronization boundary (at the coupling decrease).

Key words: 
-
Acknowledgments: 
The work was carried out with the financial support of RFBR, grant No. 2-02-17578, RAS grant No. 23, with the support of CRDF, REC-006.
Reference: 
  1. Yamada T, Fujisaka H. Stability theory оf synchronized motions in coupled oscillatory systems. Prog. Theor. Phys. 1983;69(1):32–47. DOI: 10.1143/PTP.69.32.
  2. Pikovsky AS. Interaction of strange attractors. Preprint No. 79. Gorky: Institute of Applied Physics of the USSR Academy of Sciences; 1983. 21 p. (in Russian).
  3. Pecora LM, Carrol TL. Synchronization in chaotic systems. Phys. Rev. Lett. 1990;64(8):821–824. DOI: 10.1103/PhysRevLett.64.821.
  4. Afraimovich VS, Nekorkin VI, Osipov GV, Shalfeev VD. Stability, Structures and Chaos in Nonlinear Synchronization Networks. Singapore: World Scientific; 1994. 260 p. DOI: 10.1142/2412.
  5. Hasler M, Maistrenko Y, Popovych О. Simple example оf partial synchronization of chaotic systems. Phys. Rev. Е. 1998;58(5):6843–6846. DOI: 10.1103/PhysRevE.58.6843.
  6. Maistrenko YL, Maistrenko VL, Popovich А, Mosekilde Е. Transverse instability and riddled basins in а system оf two coupled logistic maps. Phys. Rev. Е. 1998;57(3):2713–2724. DOI: 10.1103/PhysRevE.57.2713.
  7. Astakhov V, Kapitaniak T, Shabunin A, Anishchenko V. Non-bifurcational mechanism of loss of chaos synchronization in coupled nonidentical systems. Phys. Lett. А. 1999;258(2-3):99–102. DOI: 10.1016/S0375-9601(99)00291-1.
  8. Postnov D, Han SK, Kook H. Synchronization of diffusively coupled oscillators near the homoclinic bifurcation. Phys. Rev. Е. 1999;60(3):2799–2807. DOI: 10.1103/PhysRevE.60.2799.
  9. Maistrenko YL, Maistrenko VL, Popovych O, Mosekilde E. Desynchronization оf chaos in coupled logistic maps. Phys. Rev. Е. 1999;60(3):2817–2830. DOI: 10.1103/PhysRevE.60.2817.
  10. Kuznetsov S.P. Universality and scaling in the behavior of coupled Feigenbaum systems. Radiophys. Quantum Electron. 1985;28(8):681–695. DOI: 10.1007/BF01035195.
  11. Astakhov VV, Bezruchko BP, Erastova EN, Seleznev EP. Types of oscillations and their evolution in dissipatively coupled Feigenbaum systems. Sov. Phys. Tech. Phys. 1990;60(10):19–26 (in Russian).
  12. Halsey TS, Jensen MH, Kadanoff LP. et al. Fractal measures and their singularities: The characterization of strange sets. Phys.Rev. А. 1986;33(2):1141–1151. DOI: 10.1103/PhysRevA.33.1141.
  13. Kuznetsov AP, Kuznetsov SP. Critical dynamics for one-dimensional maps part 1: Feigenbaum's scenario. Izvestiya VUZ. Applied Nonlinear Dynamics. 1993;1(1):15–33 (in Russian).
Received: 
04.09.2002
Accepted: 
15.10.2002
Available online: 
24.01.2024
Published: 
30.12.2002
  • 160 reads