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Adaptive symmetry control in secure communication systems

Author

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  • Tutueva, Aleksandra
  • Moysis, Lazaros
  • Rybin, Vyacheslav
  • Zubarev, Alexander
  • Volos, Christos
  • Butusov, Denis

Abstract

Chaos-based secure communications is a broadly studied field in nonlinear dynamics. Such technique is traditionally based on chaotic synchronization between master and slave systems implemented as the transmitter and receiver. A common way to encode the message is switching the bifurcation parameters of the master system, which leads to perturbation of the dynamics and often breaks the synchronization. The time of the transient process to restore the identity of the trajectories of the master and slave systems can be unacceptably long for practical applications. Therefore, the development of techniques for fast re-synchronization of models of chaotic systems is of interest. In this paper we propose a novel technique for synchronizing finite-difference models of continuous chaotic systems through adaptive control of the so-called symmetry coefficient. We experimentally confirm that the proposed approach can be faster than the traditional control of the bifurcation parameter. In addition, we discovered that changing the symmetry coefficient in semi-implicit models leads only to a slight deformation of the stability regions of the finite-difference scheme and practically does not affect the nonlinear properties of the simulated chaotic system. The applied analysis shows that detecting a transmitted message through the modulation of the symmetry coefficient is difficult compared to the conventional approach.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003915
    DOI: 10.1016/j.chaos.2022.112181
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    References listed on IDEAS

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    1. Sharma, Vivek & Sharma, B.B. & Nath, R., 2017. "Nonlinear unknown input sliding mode observer based chaotic system synchronization and message recovery scheme with uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 51-58.
    2. 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).
    3. Denis Butusov & Aleksandra Tutueva & Petr Fedoseev & Artem Terentev & Artur Karimov, 2020. "Semi-Implicit Multistep Extrapolation ODE Solvers," Mathematics, MDPI, vol. 8(6), pages 1-18, June.
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    5. Kim, Jae-Hun & Park, Chang-Woo & Kim, Euntai & Park, Mignon, 2005. "Adaptive synchronization of T–S fuzzy chaotic systems with unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1353-1361.
    6. Yang, Yu & Ma, Xi-Kui & Zhang, Hao, 2006. "Synchronization and parameter identification of high-dimensional discrete chaotic systems via parametric adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 244-251.
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    Cited by:

    1. Ivan Babkin & Vyacheslav Rybin & Valery Andreev & Timur Karimov & Denis Butusov, 2024. "Coherent Chaotic Communication Using Generalized Runge–Kutta Method," Mathematics, MDPI, vol. 12(7), pages 1-21, March.
    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).
    3. Lai, Qiang & Chen, Zhijie, 2023. "Dynamical analysis and finite-time synchronization of grid-scroll memristive chaotic system without equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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