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Fast synchronization of symmetric Hénon maps using adaptive symmetry control

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  • Tutueva, Aleksandra V.
  • Moysis, Lazaros
  • Rybin, Vyacheslav G.
  • Kopets, Ekaterina E.
  • Volos, Christos
  • Butusov, Denis N.

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.

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  • Tutueva, Aleksandra V. & Moysis, Lazaros & Rybin, Vyacheslav G. & Kopets, Ekaterina E. & Volos, Christos & Butusov, Denis N., 2022. "Fast synchronization of symmetric Hénon maps using adaptive symmetry control," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010869
    DOI: 10.1016/j.chaos.2021.111732
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    1. Tutueva, Aleksandra & Moysis, Lazaros & Rybin, Vyacheslav & Zubarev, Alexander & Volos, Christos & Butusov, Denis, 2022. "Adaptive symmetry control in secure communication systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Ostrovskii, Valerii Yu. & Rybin, Vyacheslav G. & Karimov, Artur I. & Butusov, Denis N., 2022. "Inducing multistability in discrete chaotic systems using numerical integration with variable symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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