Izvestiya of Saratov University.


ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Astakhov V. V., Astakhov S. V., Nekhodtseva E. I., Shabunin A. V. Influence of Time-delay in the Coupling Channel on the Complete Synchronization of Chaos. Izvestiya of Saratov University. Physics , 2008, vol. 8, iss. 2, pp. 30-34. DOI: 10.18500/1817-3020-2008-8-2-30-34

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
Full text:
(downloads: 147)
Article type: 

Influence of Time-delay in the Coupling Channel on the Complete Synchronization of Chaos

Astakhov Vladimir Vladimirovich, Saratov State University
Astakhov Sergei Vladimirovich, Saratov State University
Nekhodtseva E. I., Saratov State University
Shabunin Alexey Vladimirovich, Saratov State University

In the current work the influence of delay in a coupling channel on the synchronization of regular and chotic oscillations in discrete maps and continuous time systems is studied. It is established that introduction of time delay in a discrete system prevents synchronization of chaos but allows synchronization of periodic and quasiperiodic oscillations. In a continuous time system with chaotic attractor the introduction of a small delay doesn’t make essential changes in its dynamics however the increasing of delay leads to the reverse period doubling cascade.

  1. Raddy D.V.R., Sen A., Johnston G.L. Time Delay Induced Death in Coupled Limit Cycle Oscillators // Phys. Rev. Lett. 1998. Vol. 80. P. 5109.
  2. Raddy D.V.R., Sen A., Johnston G.L. Experimetnal Evidence of Time-Delay-Induced Death in Coupled Limit-Cycle Oscillators // Phys. Rev. Lett. 2000. Vol. 85. P. 3381.
  3. Yeung M.K.S., Strogatz S.H. Time Delay in the Kuramoto Model of Coupled Oscillators // Phys. Rev. Lett. 1999. Vol. 82. P. 648.
  4. Chung T.-H., 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 / Ed. by S. Kim, K.J. Lee, W. Sung. Berlin: Springer-Verlag, 2000. P. 67–74.
  5. Astakhov V., Shabunin A., Klimshin A., Anishchenko V. In-phase and Anti-phase Complete Chaotic Synchronization in Symmetrically Coupled Discrete Maps // Discrete Dynamics in Nature and Society. 2002. Vol. 7. P. 215.
  6. Астахов В.В., Шабунин А.В., Анищенко В.С. Механизмы разрушения хаотической синхронизации в системе связанных кубических отображений // Изв. вузов. Прикладная нелинейная динамика. 1999. Т. 7, № 2. С. 3.
  7. Астахов В.В., Неходцева Е.И., Астахов С.В., Шабунин А.В. Влияние задержки в канале связи на режимы полной синхронизации хаотических систем с дискретным временем // Изв. вузов: Прикладная нелинейная динамика. 2007. Т. 15, № 5. С. 61.
  8. Anishchenko V. Dynamical Chaos: Models and Experiments. Singapore: World Scientific, 1995. 400 p.