IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v155y2022ics0960077921010869.html
   My bibliography  Save this article

Fast synchronization of symmetric Hénon maps using adaptive symmetry control

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921010869
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111732?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kajbaf, Amin & Akhaee, Mohammad Ali & Sheikhan, Mansour, 2016. "Fast synchronization of non-identical chaotic modulation-based secure systems using a modified sliding mode controller," Chaos, Solitons & Fractals, Elsevier, vol. 84(C), pages 49-57.
    2. Kuetche Mbe, E.S. & Fotsin, H.B. & Kengne, J. & Woafo, P., 2014. "Parameters estimation based adaptive Generalized Projective Synchronization (GPS) of chaotic Chua’s circuit with application to chaos communication by parametric modulation," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 27-37.
    3. Wang, Cong & Zhang, Hong-li & Fan, Wen-hui, 2017. "Generalized dislocated lag function projective synchronization of fractional order chaotic systems with fully uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 14-21.
    4. Zhili Xiong & Shaocheng Qu & Jing Luo, 2019. "Adaptive Multi-Switching Synchronization of High-Order Memristor-Based Hyperchaotic System with Unknown Parameters and Its Application in Secure Communication," Complexity, Hindawi, vol. 2019, pages 1-18, December.
    5. García-Guerrero, E.E. & Inzunza-González, E. & López-Bonilla, O.R. & Cárdenas-Valdez, J.R. & Tlelo-Cuautle, E., 2020. "Randomness improvement of chaotic maps for image encryption in a wireless communication scheme using PIC-microcontroller via Zigbee channels," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    6. 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.
    7. Tutueva, Aleksandra V. & Nepomuceno, Erivelton G. & Karimov, Artur I. & Andreev, Valery S. & Butusov, Denis N., 2020. "Adaptive chaotic maps and their application to pseudo-random numbers generation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    8. Li, Shujun & Álvarez, Gonzalo & Chen, Guanrong, 2005. "Breaking a chaos-based secure communication scheme designed by an improved modulation method," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 109-120.
    9. Durdu, Ali & Uyaroğlu, Yılmaz, 2017. "The Shortest Synchronization Time with Optimal Fractional Order Value Using a Novel Chaotic Attractor Based on Secure Communication," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 98-106.
    10. Batista, Carlos A.S. & Viana, Ricardo L., 2020. "Chaotic maps with nonlocal coupling: Lyapunov exponents, synchronization of chaos, and characterization of chimeras," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    11. Butusov, Denis N. & Karimov, Artur I. & Pyko, Nikita S. & Pyko, Svetlana A. & Bogachev, Mikhail I., 2018. "Discrete chaotic maps obtained by symmetric integration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 955-970.
    12. Aguilar-Bustos, A.Y. & Cruz-Hernández, C., 2009. "Synchronization of discrete-time hyperchaotic systems: An application in communications," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1301-1310.
    13. Tutueva, Aleksandra V. & Karimov, Artur I. & Moysis, Lazaros & Volos, Christos & Butusov, Denis N., 2020. "Construction of one-way hash functions with increased key space using adaptive chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    14. Danca, Marius-F. & Kuznetsov, Nikolay, 2017. "Parameter Switching Synchronization," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 94-102.
    15. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. Ding, Jianpeng & Lei, Youming & Xie, Jianfei & Small, Michael, 2024. "Chaos synchronization of two coupled map lattice systems using safe reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    3. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tutueva, Aleksandra V. & Karimov, Artur I. & Moysis, Lazaros & Volos, Christos & Butusov, Denis N., 2020. "Construction of one-way hash functions with increased key space using adaptive chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Trujillo-Toledo, D.A. & López-Bonilla, O.R. & García-Guerrero, E.E. & Tlelo-Cuautle, E. & López-Mancilla, D. & Guillén-Fernández, O. & Inzunza-González, E., 2021. "Real-time RGB image encryption for IoT applications using enhanced sequences from chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    3. 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.
    4. Rasool, Masrat & Belhaouari, Samir Brahim, 2023. "From Collatz Conjecture to chaos and hash function," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    5. Hanshuo Qiu & Xiangzi Zhang & Huaixiao Yue & Jizhao Liu, 2023. "A Novel Eighth-Order Hyperchaotic System and Its Application in Image Encryption," Mathematics, MDPI, vol. 11(19), pages 1-29, September.
    6. Runzi Luo & Jiaojiao Fu & Haipeng Su, 2019. "The Exponential Stabilization of a Class of n-D Chaotic Systems via the Exact Solution Method," Complexity, Hindawi, vol. 2019, pages 1-7, May.
    7. 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).
    8. 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).
    9. Bowen Zhang & Lingfeng Liu, 2023. "Chaos-Based Image Encryption: Review, Application, and Challenges," Mathematics, MDPI, vol. 11(11), pages 1-39, June.
    10. Xuan-Bing Yang & Yi-Gang He & Chun-Lai Li, 2018. "Dynamics Feature and Synchronization of a Robust Fractional-Order Chaotic System," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    11. Vafamand, Navid & Khorshidi, Shapour & Khayatian, Alireza, 2018. "Secure communication for non-ideal channel via robust TS fuzzy observer-based hyperchaotic synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 116-124.
    12. Chenchen Peng & Haiyi Yang & Anqing Yang & Ling Ren, 2024. "A New Observer Design for the Joint Estimation of States and Unknown Inputs for a Class of Nonlinear Fractional-Order Systems," Mathematics, MDPI, vol. 12(8), pages 1-12, April.
    13. Shihong Zhang & Hu Shi & Baizhong Wang & Chunlu Ma & Qinghua Li, 2024. "A Dynamic Hierarchical Improved Tyrannosaurus Optimization Algorithm with Hybrid Topology Structure," Mathematics, MDPI, vol. 12(10), pages 1-35, May.
    14. Zaher, Ashraf A., 2009. "An improved chaos-based secure communication technique using a novel encryption function with an embedded cipher key," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2804-2814.
    15. Li, Xuejun & Mou, Jun & Banerjee, Santo & Wang, Zhisen & Cao, Yinghong, 2022. "Design and DSP implementation of a fractional-order detuned laser hyperchaotic circuit with applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    16. Yan, Yanjun & Chen, Kai & Zhao, Yijiu & Wang, Houjun & Xu, Bo & Wang, Yifan, 2024. "An innovative orthogonal matrix based on nonlinear chaotic system for compressive sensing," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    17. Bezerra, João Inácio Moreira & Machado, Gustavo & Molter, Alexandre & Soares, Rafael Iankowski & Camargo, Vinícius, 2023. "A novel simultaneous permutation–diffusion image encryption scheme based on a discrete space map," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    18. Coelho, Leandro dos Santos & Bernert, Diego Luis de Andrade, 2009. "PID control design for chaotic synchronization using a tribes optimization approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 634-640.
    19. Dong, Youheng & Zhao, Geng, 2021. "A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    20. Sharma, B.B. & Kar, I.N., 2011. "Stabilization and tracking controller for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 902-913.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010869. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.