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Secure Communication of Fractional Complex Chaotic Systems Based on Fractional Difference Function Synchronization

Author

Listed:
  • Jiaxun Liu
  • Zuoxun Wang
  • Minglei Shu
  • Fangfang Zhang
  • Sen Leng
  • Xiaohui Sun

Abstract

Fractional complex chaotic systems have attracted great interest recently. However, most of scholars adopted integer real chaotic system and fractional real and integer complex chaotic systems to improve the security of communication. In this paper, the advantages of fractional complex chaotic synchronization ( FCCS ) in secure communication are firstly demonstrated. To begin with, we propose the definition of fractional difference function synchronization ( FDFS ) according to difference function synchronization ( DFS ) of integer complex chaotic systems. FDFS makes communication secure based on FCCS possible. Then we design corresponding controller and present a general communication scheme based on FDFS . Finally, we respectively accomplish simulations which transmit analog signal, digital signal, voice signal, and image signal. Especially for image signal, we give a novel image cryptosystem based on FDFS . The results demonstrate the superiority and good performances of FDFS in secure communication.

Suggested Citation

  • Jiaxun Liu & Zuoxun Wang & Minglei Shu & Fangfang Zhang & Sen Leng & Xiaohui Sun, 2019. "Secure Communication of Fractional Complex Chaotic Systems Based on Fractional Difference Function Synchronization," Complexity, Hindawi, vol. 2019, pages 1-10, August.
    • Handle: RePEc:hin:complx:7242791
    DOI: 10.1155/2019/7242791
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    References listed on IDEAS

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    1. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
    2. Mahmoud, Emad E. & Abo-Dahab, S.M., 2018. "Dynamical properties and complex anti synchronization with applications to secure communications for a novel chaotic complex nonlinear model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 273-284.
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    Cited by:

    1. Fangfang Zhang & Rui Gao & Zhe Huang & Cuimei Jiang & Yawen Chen & Haibo Zhang, 2022. "Complex Modified Projective Difference Function Synchronization of Coupled Complex Chaotic Systems for Secure Communication in WSNs," Mathematics, MDPI, vol. 10(7), pages 1-14, April.
    2. Chih-Hsueh Lin & Chia-Wei Ho & Guo-Hsin Hu & Baswanth Sreeramaneni & Jun-Juh Yan, 2021. "Secure Data Transmission Based on Adaptive Chattering-Free Sliding Mode Synchronization of Unified Chaotic Systems," Mathematics, MDPI, vol. 9(21), pages 1-11, October.
    3. Liu, Jianjun & Zhai, Rui & Liu, Yuhan & Li, Wenliang & Wang, Bingzhe & Huang, Liyuan, 2021. "A quasi fractional order gradient descent method with adaptive stepsize and its application in system identification," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    4. Zhang, Fangfang & Zhang, Shuaihu & Chen, Guanrong & Li, Chunbiao & Li, Zhengfeng & Pan, Changchun, 2022. "Special attractors and dynamic transport of the hybrid-order complex Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Pengyu Li & Juan Du & Shouliang Li & Yazhao Zheng & Bowen Jia, 2019. "The Synchronization of N Cascade-Coupled Chaotic Systems," Complexity, Hindawi, vol. 2019, pages 1-10, December.

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