Fast synchronization of symmetric Hénon maps using adaptive symmetry control. (February 2022) - Tutueva, Aleksandra V.; Moysis, Lazaros; Rybin, Vyacheslav G.; Kopets, Ekaterina E.; Volos, Christos; Butusov, Denis N.
Highlights: A new approach for adaptive synchronization of symmetric discrete chaotic maps based on symmetry control is considered. It is experimentally shown that adaptive synchronization via symmetry control is faster than its parameter-based counterpart. The discovered ability to synchronize discrete maps with higher accuracy reveals potentially robust foundations for the development of secure communication systems. Abstract: The article discusses the possibility of synchronizing adaptive discrete chaotic maps through the control of the symmetry coefficient. Since a change in the symmetry coefficient in symmetric chaotic maps possesses a much less influence on the system oscillation mode than a change in nonlinearity parameters, we assume that the synchronization of such systems can be achieved in a small number of iterations. To experimentally examine this hypothesis, we studied three cases of adaptive synchronization feedback controllers for the conventional Hénon map and adaptive Hénon map. We found that synchronization occurs faster while the symmetry coefficient is controlled by comparing the synchronization times in all considered cases. Averagely, an accurate estimate of the adaptive coefficient is achieved after 3–5 iterations. Applying this approach to the communication systems based on modulation through switching parameters of chaotic systems can significantly reduce the transient processes inherent in this method. The numerical experiments show that it is possible to decrease the transmission time by more than 25%, even in the case of short messages.