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A new fractional-order hyperchaotic system and its modified projective synchronization

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  • Gao, Yuan
  • Liang, Chenghua
  • Wu, Qiqi
  • Yuan, Haiying

Abstract

A new four-dimensional (4D) autonomous hyperchaotic system is investigated at first. It is found that the fractional-order version of the system goes through periodical status to chaos and hyperchaos while the order number q is increased. We verify the realizability of the new fractional-order hyperchaotic system via a practical electronic circuit. Furthermore, an active integral sliding mode control (ISMC) scheme is proposed to achieve the modified projective synchronization (MPS) of two different fractional-order hyperchaotic systems. The sliding mode controller of MPS is derived based on the stability theory of the fractional-order system and Lyapunov stability theorem. The presented method can guarantee the synchronization error asymptotically stable and enhance the robustness of MPS. Finally, the MPS between the fractional-order Chen hyperchaotic system and the new fractional-order hyperchaotic system is considered as an example, our simulation results demonstrate the effectiveness and robustness of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:76:y:2015:i:c:p:190-204
    DOI: 10.1016/j.chaos.2015.04.003
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    2. Singh, Jay Prakash & Roy, B.K., 2016. "The nature of Lyapunov exponents is (+, +, −, −). Is it a hyperchaotic system?," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 73-85.
    3. 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.
    4. Chen, Liping & Pan, Wei & Wang, Kunpeng & Wu, Ranchao & Machado, J. A. Tenreiro & Lopes, António M., 2017. "Generation of a family of fractional order hyper-chaotic multi-scroll attractors," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 244-255.
    5. Borah, Manashita & Roy, Binoy Krishna, 2020. "Systematic construction of high dimensional fractional-order hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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