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A note on the fractional-order Chua’s system

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  • Petráš, Ivo

Abstract

This paper deals with fractional-order Chua’s system. It is based on the well-known concept of the Chua’s oscillator, where mathematical model of the Chua’s system consists the fractional-order derivatives. We present the method to derive such kind of the fractional-order model. The fractional-order Chua’s system with a total order less than three, which exhibits chaos as well as other nonlinear behavior, is presented. Numerical experimental example and real measurement are shown to verify the theoretical results.

Suggested Citation

  • Petráš, Ivo, 2008. "A note on the fractional-order Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 140-147.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:1:p:140-147
    DOI: 10.1016/j.chaos.2006.10.054
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    References listed on IDEAS

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    1. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    2. Lu, Jun Guo, 2005. "Chaotic dynamics and synchronization of fractional-order Arneodo’s systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1125-1133.
    3. Gao, Xin & Yu, Juebang, 2005. "Chaos in the fractional order periodically forced complex Duffing’s oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1097-1104.
    4. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    5. 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.
    6. Ahmad, Wajdi M., 2005. "Hyperchaos in fractional order nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1459-1465.
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