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

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Astakhov V. V., Nehodceva E. I., Astahov S. V., Shabunin A. V. Influence of time delay coupling on the complete synchronization of chaos in chaotic systems with discrete time. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 5, pp. 61-67. DOI: 10.18500/0869-6632-2007-15-5-61-67

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Influence of time delay coupling on the complete synchronization of chaos in chaotic systems with discrete time

Astakhov Vladimir Vladimirovich, Yuri Gagarin State Technical University of Saratov
Nehodceva Ekaterina Igorevna, Saratov State University
Astahov Sergej Vladimirovich, Saratov State University
Shabunin Aleksej Vladimirovich, Saratov State University

In the work the influence of time delay of coupling on the complete synchronization of chaos in an interacting systems with discrete time is studied. The system’s behavior is considered in dependence on coupling coefficient value and delay time value. It is established that coupling with time delay prevents appearance of the complete synchronization of chaos, however it allows the synchronization of periodic and quasi-periodic oscillations.

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  1. Ramana Reddy DVR, Sen A, Johnston GL. Time delay induced death in coupled limit cycle oscillators. Phys. Rev. Lett. 1998;80:5109–5112. DOI: 10.1103/PhysRevLett.80.5109.
  2. Ramana Raddy DV, Sen A, Johnston GL. Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators. Phys. Rev. Lett. 2000;85:3381–3384. DOI: 10.1103/PhysRevLett.85.3381.
  3. Yeung MKS, Strogatz SH. Time delay in the Кuramoto model of coupled oscillators. Phys. Rev. Lett. 1999;82:648–651. DOI: 10.1103/PhysRevLett.82.648
  4. Chung TH, Kim S. Spatio-temporal dynamics in locally coupled Ginzburg-Landau oscillator chain with time delay. Stochastic Dynamics and Pattern Formation in Biological and Complex Systems. Edited by Kim S, Lee KJ, Sung W. Berlin: Springer-Verlag. 2000;501:67–74. DOI: 10.1063/1.59952.
  5. Jiang Y. Globally coupled maps with time delay interactions. Physics Letters A. 2000;267:342–349.
  6. Astakhov V, Shabunin A, Klimshin A, Anishchenko V. In-phase and antiphase complete chaotic synchronization in symmetrically coupled discrete maps. Discrete Dynamics in Nature and Society. 2002;7:215–219.
  7. Astakhov VV, Shabunin AV, Anishchenko VS. Mechanisms of chaotic synchronization destruction in coupled cubic maps system. Izvestiya VUZ. Applied Nonlinear Dynamics. 1999;7(2):3–11 (in Russian).
  8. Koblyansky SA. Management of multistable states using synchronization. Collection «Nonlinear days for the young in Saratov – 2007». (in Russian).
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