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Chaos in the fractional-order complex Lorenz system and its synchronization

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Abstract

In this article, a novel dynamic system, the fractional-order complex Lorenz system, is proposed. Dynamic behaviors of a fractional-order chaotic system in complex space are investigated for the first time. Chaotic regions and periodic windows are explored as well as different types of motion shown along the routes to chaos. Numerical experiments by means of phase portraits, bifurcation diagrams and the largest Lyapunov exponent are involved. A new method to search the lowest order of the fractional-order system is discussed. Based on the above result, a synchronization scheme in fractional-order complex Lorenz systems is presented and the corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Nos: 61173183, 60973152, and 60573172), the Superior University Doctor Subject Special Scientific Research Foundation of China (No: 20070141014), Program for Liaoning Excellent Talents in University (No: LR2012003), the National Natural Science Foundation of Liaoning province (No: 20082165) and the Fundamental Research Funds for the Central Universities (No: DUT12JB06).

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  1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Chao Luo & Xingyuan Wang

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  1. Chao Luo
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  2. Xingyuan Wang
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Correspondence to Xingyuan Wang.

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Luo, C., Wang, X. Chaos in the fractional-order complex Lorenz system and its synchronization. Nonlinear Dyn 71, 241–257 (2013). https://doi.org/10.1007/s11071-012-0656-z

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