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Generalized projective synchronization of the fractional-order Chen hyperchaotic system

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Abstract

In this paper, we numerically investigate the hyperchaotic behaviors in the fractional-order Chen hyperchaotic systems. By utilizing the fractional calculus techniques, we find that hyperchaos exists in the fractional-order Chen hyperchaotic system with the order less than 4. We found that the lowest order for hyperchaos to have in this system is 3.72. Our results are validated by the existence of two positive Lyapunov exponents. The generalized projective synchronization method is also presented for synchronizing the fractional-order Chen hyperchaotic systems. The present technique is based on the Laplace transform theory. This simple and theoretically rigorous synchronization approach enables synchronization of fractional-order hyperchaotic systems to be achieved and does not require the computation of the conditional Lyapunov exponents. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.

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  1. Computing Center, Henan University, Kaifeng, 475000, China

    Xiangjun Wu & Yang Lu

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  1. Xiangjun Wu
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  2. Yang Lu
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Wu, X., Lu, Y. Generalized projective synchronization of the fractional-order Chen hyperchaotic system. Nonlinear Dyn 57, 25–35 (2009). https://doi.org/10.1007/s11071-008-9416-5

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