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Generalized synchronization in discrete maps. New point of view on weak and strong synchronization

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  • Koronovskii, Alexey A.
  • Moskalenko, Olga I.
  • Shurygina, Svetlana A.
  • Hramov, Alexander E.

Abstract

In the present Letter we show that the concept of the generalized synchronization regime in discrete maps needs refining in the same way as it has been done for the flow systems Koronovskii et al. [Koronovskii AA, Moskalenko OI, Hramov AE. Nearest neighbors, phase tubes, and generalized synchronization. Phys Rev E 2011;84:037201]. We have shown that, in the general case, when the relationship between state vectors of the interacting chaotic maps are considered, the prehistory must be taken into account. We extend the phase tube approach to the systems with a discrete time coupled both unidirectionally and mutually and analyze the essence of the generalized synchronization by means of this technique. Obtained results show that the division of the generalized synchronization into the weak and the strong ones also must be reconsidered. Unidirectionally coupled logistic maps and Hénon maps coupled mutually are used as sample systems.

Suggested Citation

  • Koronovskii, Alexey A. & Moskalenko, Olga I. & Shurygina, Svetlana A. & Hramov, Alexander E., 2013. "Generalized synchronization in discrete maps. New point of view on weak and strong synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 12-18.
    • Handle: RePEc:eee:chsofr:v:46:y:2013:i:c:p:12-18
    DOI: 10.1016/j.chaos.2012.10.004
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    References listed on IDEAS

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    1. Leon Glass, 2001. "Synchronization and rhythmic processes in physiology," Nature, Nature, vol. 410(6825), pages 277-284, March.
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    Cited by:

    1. 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).
    2. Moskalenko, Olga I. & Koronovskii, Alexey A. & Plotnikova, Anastasiya D., 2021. "Peculiarities of generalized synchronization in unidirectionally and mutually coupled time-delayed systems," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Koronovskii, Alexey A. & Moskalenko, Olga I. & Ponomarenko, Vladimir I. & Prokhorov, Mikhail D. & Hramov, Alexander E., 2016. "Binary generalized synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 133-139.

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