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

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):
(downloads: 178)
Article type: 

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

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

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: 
  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.
Short text (in English):
(downloads: 65)