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

For citation:

Astakhov V. V., Shabunin A. V., Stalmahov P. A. Bifurcational mechanisms of destruction of antiphase chaotic synchronization in coupled discrete-time systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 6, pp. 100-111. DOI: 10.18500/0869-6632-2006-14-6-100-111

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2006-14-6-100-111

Bifurcational mechanisms of destruction of antiphase chaotic synchronization in coupled discrete-time systems

Autors: 
Astakhov Vladimir Vladimirovich, Yuri Gagarin State Technical University of Saratov
Shabunin Aleksej Vladimirovich, Saratov State University
Stalmahov Petr Andreevich, Saratov State University
Abstract: 

Bifurcational mechanisms responsible for destruction of antiphase synchronization of chaos are studied. Two cubic discrete maps with symmetric diffusive coupling and additional control term are used as a model. Phenomenon of synchronization formation and destruction are explored in connection with bifurcations of principal periodic orbits embedded in the chaotic attractor.

Key words: 
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Reference: 
  1. Kuznetsov YuI, Landa PS, Olkhovoi AF, Perminov SM. On the relation between the synchronization amplitude threshold and entropy in the stochastic self-oscillatory systems. Dokl. Akad. Nauk SSSR. 1985;281(2):291–294.
  2. Anishchenko VS, Vadivasova TE, Postnov DE, Safonova MA. Forced and mutual synchronization of chaos. Radiotekhnika i Elektronika. 1991;36(2):338–351.
  3. Rosenblum MG, Pikovsky AS, Kurths J. Phase synchronization of chaotic oscillators. Phys Rev Lett. 1996;76(11):1804–1807. DOI: 10.1103/PhysRevLett.76.1804.
  4. Abarbanel HDI, Rulkov NF, Sushchik MM. Generalized synchronization of chaos: The auxiliary system approach. Phys. Rev. E. 1996;53(5):4528–4535. DOI: 10.1103/PHYSREVE.53.4528.
  5. Fujisaka H, Yamada T. Stability theory of synchronized motion in coupled-oscillator systems. Progress of theoretical physics. 1983;69(1):32–47. DOI: 10.1143/PTP.69.32.
  6. Pikovsky AS. On the interaction of strange attractors. Preprint No. 79, Gorky: IPF AS of the USSR; 1983. 21 p. (In Russian).
  7. Kuznetsov SP. Universality and scaling in the behavior of coupled Feigenbaum systems. Radiophys Quantum Electron. 1985;28(8):681–695. DOI: 10.1007/BF01035195.
  8. Afraimovich VS, Verichev NN, Rabinovich MI. Stochastic synchronization of oscillation in dissipative systems. Radiophys Quantum Electron. 1986;29(9):795–803. DOI: 10.1007/BF01034476.
  9. Cao L-Y, Lai Y-C. Antiphase synchronism in chaotic systems. Phys. Rev. E. 1998;58(1):382–386. DOI: 10.1103/PHYSREVE.58.382.
  10. Astakhov V, Shabunin A, Stalmakhov P. Multistability, in-phase and anti-phase chaos synchronisation in period-doubling systems. Izvestiya VUZ. Applied Nonlinear Dynamics. 2002;10(3):63–79.
  11. Astakhov V, Shabunin A, Kapitaniak T, Anishchenko V. Loss of chaos synchronization through the sequence of bifurcations of saddle periodic orbits. Physical Review Letters. 1997;79(6):1014–1017. DOI: 10.1103/PhysRevLett.79.1014.
  12. Ashvin P, Buescu J, Stewart I. Bubbling of attractors and synchronization of chaotic oscillators. Physics Letters A. 1994;193:126–139.
Received: 
28.07.2006
Accepted: 
28.07.2006
Published: 
29.12.2006
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