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Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems

Author

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  • Seng-Kin Lao
  • Lap-Mou Tam
  • Hsien-Keng Chen
  • Long-Jye Sheu

Abstract

A hybrid stability checking method is proposed to verify the establishment of synchronization between two hyperchaotic systems. During the design stage of a synchronization scheme for chaotic fractional-order systems, a problem is sometimes encountered. In order to ensure the stability of the error signal between two fractional-order systems, the arguments of all eigenvalues of the Jacobian matrix of the erroneous system should be within a region defined in Matignon’s theorem. Sometimes, the arguments depend on the state variables of the driving system, which makes it difficult to prove the stability. We propose a new and efficient hybrid method to verify the stability in this situation. The passivity-based control scheme for synchronization of two hyperchaotic fractional-order Chen-Lee systems is provided as an example. Theoretical analysis of the proposed method is validated by numerical simulation in time domain and examined in frequency domain via electronic circuits.

Suggested Citation

  • Seng-Kin Lao & Lap-Mou Tam & Hsien-Keng Chen & Long-Jye Sheu, 2014. "Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, April.
    • Handle: RePEc:hin:jnlaaa:316368
    DOI: 10.1155/2014/316368
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    Cited by:

    1. Kengne, Romanic & Tchitnga, Robert & Mabekou, Sandrine & Tekam, Blaise Raoul Wafo & Soh, Guy Blondeau & Fomethe, Anaclet, 2018. "On the relay coupling of three fractional-order oscillators with time-delay consideration: Global and cluster synchronizations," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 6-17.
    2. Singh, Jay Prakash & Roy, Binoy Krishna & Jafari, Sajad, 2018. "New family of 4-D hyperchaotic and chaotic systems with quadric surfaces of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 243-257.

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