Izvestiya of Saratov University.

Physics

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 Sarat. Univ. 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: 
23.12.2008
Full text:
(downloads: 115)
Language: 
Russian
Heading: 
Article type: 
Article
UDC: 
517.9

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

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

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.

Reference: 
  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.
Received: 
18.07.2008
Accepted: 
09.11.2008
Published: 
23.12.2008