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Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen–Lee systems

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Abstract

Recently, the fractional-order Chen–Lee system was proven to exhibit chaos by the presence of a positive Lyapunov exponent. However, the existence of chaos in fractional-order Chen–Lee systems has never been theoretically proven in the literature. Moreover, synchronization of chaotic fractional-order systems was extensively studied through numerical simulations in some of the literature, but a theoretical analysis is still lacking. Therefore, we devoted ourselves to investigating the theoretical basis of chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen–Lee systems in this paper. Based on the stability theorems of fractional-order systems, the necessary conditions for the existence of chaos and the controllers for hybrid projective synchronization were derived. The numerical simulations show coincidence with the theoretical results.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hsiuping Institute of Technology, Dali City, Taichung County, Taiwan

    Ching-Ming Chang & Hsien-Keng Chen

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  1. Ching-Ming Chang
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  2. Hsien-Keng Chen
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Correspondence to Hsien-Keng Chen.

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Chang, CM., Chen, HK. Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen–Lee systems. Nonlinear Dyn 62, 851–858 (2010). https://doi.org/10.1007/s11071-010-9767-6

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