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Chaos synchronization of fractional chaotic maps based on the stability condition

Author

Listed:
  • Wu, Guo-Cheng
  • Baleanu, Dumitru
  • Xie, He-Ping
  • Chen, Fu-Lai

Abstract

In the fractional calculus, one of the main challenges is to find suitable models which are properly described by discrete derivatives with memory. Fractional Logistic map and fractional Lorenz maps of Riemann–Liouville type are proposed in this paper. The general chaotic behaviors are investigated in comparison with the Caputo one. Chaos synchronization is designed according to the stability results. The numerical results show the method’s effectiveness and fractional chaotic map’s potential role for secure communication.

Suggested Citation

  • Wu, Guo-Cheng & Baleanu, Dumitru & Xie, He-Ping & Chen, Fu-Lai, 2016. "Chaos synchronization of fractional chaotic maps based on the stability condition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 374-383.
    • Handle: RePEc:eee:phsmap:v:460:y:2016:i:c:p:374-383
    DOI: 10.1016/j.physa.2016.05.045
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    References listed on IDEAS

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    1. Chao Luo & Xingyuan Wang, 2013. "Chaos Generated From The Fractional-Order Complex Chen System And Its Application To Digital Secure Communication," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 1-23.
    2. Deng, W.H. & Li, C.P., 2005. "Chaos synchronization of the fractional Lü system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 61-72.
    3. Li, C.P. & Deng, W.H. & Xu, D., 2006. "Chaos synchronization of the Chua system with a fractional order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 171-185.
    4. Behnia, S. & Akhshani, A. & Mahmodi, H. & Akhavan, A., 2008. "A novel algorithm for image encryption based on mixture of chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 408-419.
    5. Yu, Yongguang & Li, Han-Xiong, 2008. "The synchronization of fractional-order Rössler hyperchaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1393-1403.
    6. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2008. "Synchronization of chaotic fractional-order systems via active sliding mode controller," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 57-70.
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