Discrete Dynamics in Nature and Society
Volume 7 (2002), Issue 4, Pages 215-229

In-phase and antiphase complete chaotic synchronization in symmetrically coupled discrete maps

Vladimir Astakhov, Alexey Shabunin, Alexander Klimshin, and Vadim Anishchenko

Radiophysics and Nonlinear Dynamics Department, Saratov State University, Astrakhanskaya, 83, Saratov 410026, Russia

Received 21 September 2000

Copyright © 2002 Vladimir Astakhov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider in-phase and antiphase synchronization of chaos in a system of coupled cubic maps. Regions of stability and robustness of the regime of in-phase complete synchronization was found. It was demonstrated that the loss of the synchronization is accompanied by bubbling and riddling phenomena. The mechanisms of these phenomena are connected with bifurcations of the main family of periodic orbits and orbits appeared from them. We found that in spite of the in-phase synchronization, the antiphase self-synchronization of chaos is impossible for discrete maps with symmetric diffusive coupling. For achieving antiphase synchronization we used method of controlled synchronization by addition feedback. The region of the controlled antiphase synchronization and phenomena which accompany the loss of the synchronization are presented.