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A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

Author

Listed:
  • Zain-Aldeen S. A. Rahman

    (Department of Electrical Techniques, Technical Institute/Qurna, Southern Technical University, Basra 61016, Iraq
    Department of Electrical Engineering, College of Engineering, University of Basrah, Basra 61004, Iraq)

  • Basil H. Jasim

    (Department of Electrical Engineering, College of Engineering, University of Basrah, Basra 61004, Iraq)

  • Yasir I. A. Al-Yasir

    (Biomedical and Electronics Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford BD7 1DP, UK)

  • Yim-Fun Hu

    (Biomedical and Electronics Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford BD7 1DP, UK)

  • Raed A. Abd-Alhameed

    (Biomedical and Electronics Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford BD7 1DP, UK)

  • Bilal Naji Alhasnawi

    (Department of Electrical Engineering, College of Engineering, University of Basrah, Basra 61004, Iraq)

Abstract

This article presents a novel four-dimensional autonomous fractional-order chaotic system (FOCS) with multi-nonlinearity terms. Several dynamics, such as the chaotic attractors, equilibrium points, fractal dimension, Lyapunov exponent, and bifurcation diagrams of this new FOCS, are studied analytically and numerically. Adaptive control laws are derived based on Lyapunov theory to achieve chaos synchronization between two identical new FOCSs with an uncertain parameter. For these two identical FOCSs, one represents the master and the other is the slave. The uncertain parameter in the slave side was estimated corresponding to the equivalent master parameter. Next, this FOCS and its synchronization were realized by a feasible electronic circuit and tested using Multisim software. In addition, a microcontroller (Arduino Due) was used to implement the suggested system and the developed synchronization technique to demonstrate its digital applicability in real-world applications. Furthermore, based on the developed synchronization mechanism, a secure communication scheme was constructed. Finally, the security analysis metric tests were investigated through histograms and spectrograms analysis to confirm the security strength of the employed communication system. Numerical simulations demonstrate the validity and possibility of using this new FOCS in high-level security communication systems. Furthermore, the secure communication system is highly resistant to pirate attacks. A good agreement between simulation and experimental results is obtained, showing that the new FOCS can be used in real-world applications.

Suggested Citation

  • Zain-Aldeen S. A. Rahman & Basil H. Jasim & Yasir I. A. Al-Yasir & Yim-Fun Hu & Raed A. Abd-Alhameed & Bilal Naji Alhasnawi, 2021. "A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications," Mathematics, MDPI, vol. 9(20), pages 1-25, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2593-:d:657107
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    References listed on IDEAS

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    1. Hayette Gatfaoui & Philippe de Peretti, 2019. "Testing for non-chaoticity under noisy dynamics using the largest Lyapunov exponent," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02388420, HAL.
    2. Liu, Tianming & Yan, Huizhen & Banerjee, Santo & Mou, Jun, 2021. "A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Eshaghi, Shiva & Khoshsiar Ghaziani, Reza & Ansari, Alireza, 2020. "Hopf bifurcation, chaos control and synchronization of a chaotic fractional-order system with chaos entanglement function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 321-340.
    4. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Somayeh Hashemi & Mohammad Ali Pourmina & Saleh Mobayen & Mahdi R. Alagheband, 2020. "Design of a secure communication system between base transmitter station and mobile equipment based on finite-time chaos synchronisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(11), pages 1969-1986, July.
    6. Cao, Yanli, 2020. "Chaotic synchronization based on fractional order calculus financial system," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    7. Dutta, Maitreyee & Roy, Binoy Krishna, 2020. "A new fractional-order system displaying coexisting multiwing attractors; its synchronisation and circuit simulation," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    8. Vasily E. Tarasov, 2020. "Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 8(5), pages 1-3, April.
    9. Jian Yuan & Bao Shi & Xiaoyun Zeng & Wenqiang Ji & Tetie Pan, 2013. "Sliding Mode Control of the Fractional-Order Unified Chaotic System," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, November.
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