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Practically feasible heuristic algorithm for time-reversible synchronization of chaotic oscillators

Author

Listed:
  • Babkin, Ivan
  • Rybin, Vyacheslav
  • Karimov, Artur
  • Butusov, Denis

Abstract

Time-reversible synchronization is a novel efficient method for synchronizing chaotic dynamics. This technique uses the time-reversibility of finite-difference models obtained by symmetric numerical integrators to achieve the superexponential convergence of the trajectories of synchronized systems. However, the straightforward application of time-reversible synchronization meets significant limitations, since the real convergence of this algorithm highly depends on the choice of starting point, window length, etc. This prevents time-reversible synchronization from replacing the conventional Pecora–Carroll method in many practical applications. In the current study, we suggest a simple and versatile algorithm of time-reversible synchronization for a case of two or multiple chaotic oscillators based on heuristic rules. Several chaotic systems, namely Sprott Case L, Chen chaotic flow, and Sprott Case B, are considered as test examples to investigate the proposed synchronization method. Analog circuit implementation and its synchronization with the re-identified Case B system are performed as an additional experiment illustrating the applicability of the proposed approach to the hybrid analog-to-digital synchronization case. The experiments show that the proposed heuristic time-reversible synchronization method outperforms the classical Pecora–Carroll approach in terms of synchronization rate for all considered cases, exhibiting an example of super-exponential synchronization. Possible applications of the proposed algorithm include, but are not limited to, chaotic communications, chaotic sensors, rapid data encryption algorithms, and simulations based on complex networks of synchronized oscillators.

Suggested Citation

  • Babkin, Ivan & Rybin, Vyacheslav & Karimov, Artur & Butusov, Denis, 2026. "Practically feasible heuristic algorithm for time-reversible synchronization of chaotic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925014833
    DOI: 10.1016/j.chaos.2025.117470
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    References listed on IDEAS

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    1. Artur Karimov & Vyacheslav Rybin & Ivan Babkin & Timur Karimov & Veronika Ponomareva & Denis Butusov, 2025. "Time-Reversible Synchronization of Analog and Digital Chaotic Systems," Mathematics, MDPI, vol. 13(9), pages 1-20, April.
    2. Setoudeh, Farbod & Dezhdar, Mohammad Matin & Najafi, M., 2022. "Nonlinear analysis and chaos synchronization of a memristive-based chaotic system using adaptive control technique in noisy environments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
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