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Circuit simulation for synchronization of a fractional-order and integer-order chaotic system

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Abstract

We design a new three-dimensional double-wing fractional-order chaotic system with three quadratic terms, confirmed by numerical simulation and circuit implementation. We then study the synchronization between the new double-wing fractional-order chaotic system and different Lorenz systems with different structures. In the process of the synchronization, the definition of ‘the simplest response system’ and the practical method of designing the circuit have been originally proposed. The circuit of ‘the simplest response system’ (even the simplest incommensurate-order response system), holding different structures with the drive system, of any one integral or fractional drive system now can be designed effectively and sufficiently. Our results are supported by numerical simulation and circuit implementation.

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Acknowledgements

This wok was supported by the scientific research foundation of National Natural Science Foundation (51109180), the National Science & Technology Supporting Plan from the Ministry of Science & Technology of China (2011BAD29B08) and the “111” Project from the Ministry of Education of the P.R. of China and the State Administration of Foreign Experts Affairs of the P.R. of China (B12007).

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Authors and Affiliations

  1. Department of Electrical Engineering, Northwest A&F University, Shaanxi Yangling, 712100, P.R. China

    Diyi Chen & Xiaoyi Ma

  2. School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ, 85287, USA

    Diyi Chen

  3. Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Cong Wu

  4. School of Electrical, Electronic and Computer Engineering, University of Western Australia, Perth, WA, 6009, Australia

    Herbert H. C. Iu

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  1. Diyi Chen
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  2. Cong Wu
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  3. Herbert H. C. Iu
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  4. Xiaoyi Ma
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Correspondence to Diyi Chen.

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Chen, D., Wu, C., Iu, H.H.C. et al. Circuit simulation for synchronization of a fractional-order and integer-order chaotic system. Nonlinear Dyn 73, 1671–1686 (2013). https://doi.org/10.1007/s11071-013-0894-8

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  • DOI: https://doi.org/10.1007/s11071-013-0894-8

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