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Dynamic Analysis of Complex Synchronization Schemes between Integer Order and Fractional Order Chaotic Systems with Different Dimensions

Author

Listed:
  • Adel Ouannas
  • Xiong Wang
  • Viet-Thanh Pham
  • Toufik Ziar

Abstract

We present new approaches to synchronize different dimensional master and slave systems described by integer order and fractional order differential equations. Based on fractional order Lyapunov approach and integer order Lyapunov stability method, effective control schemes to rigorously study the coexistence of some synchronization types between integer order and fractional order chaotic systems with different dimensions are introduced. Numerical examples are used to validate the theoretical results and to verify the effectiveness of the proposed schemes.

Suggested Citation

  • Adel Ouannas & Xiong Wang & Viet-Thanh Pham & Toufik Ziar, 2017. "Dynamic Analysis of Complex Synchronization Schemes between Integer Order and Fractional Order Chaotic Systems with Different Dimensions," Complexity, Hindawi, vol. 2017, pages 1-12, June.
    • Handle: RePEc:hin:complx:4948392
    DOI: 10.1155/2017/4948392
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    References listed on IDEAS

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    1. Gao, Yuan & Liang, Chenghua & Wu, Qiqi & Yuan, Haiying, 2015. "A new fractional-order hyperchaotic system and its modified projective synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 190-204.
    2. Yan-Ping Wu & Guo-Dong Wang, 2013. "Synchronization between Fractional-Order and Integer-Order Hyperchaotic Systems via Sliding Mode Controller," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, March.
    3. Shih-Yu Li & Shi-An Chen & Chin-Teng Lin & Li-Wei Ko & Cheng-Hsiung Yang & Heng-Hui Chen, 2015. "Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-14, April.
    4. Karthikeyan Rajagopal & Laarem Guessas & Anitha Karthikeyan & Ashokkumar Srinivasan & Girma Adam, 2017. "Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization," Complexity, Hindawi, vol. 2017, pages 1-19, March.
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    Cited by:

    1. Ouannas, Adel & Odibat, Zaid & Hayat, Tasawar, 2017. "Fractional analysis of co-existence of some types of chaos synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 215-223.
    2. 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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