Although a large number of hidden chaotic attractors have been studied in recent years, most studies only refer to integer-order chaotic systems and neglect the relationships among chaotic attractors. In this paper, we first extend LE1 of sprott from integer-order chaotic systems to fractional-order chaotic systems, and we add two constant controllers which could produce a novel fractional-order chaotic system with hidden chaotic attractors. Second, we discuss its complicated dynamic characteristics with the help of projection pictures and bifurcation diagrams. The new fractional-order chaotic system can exhibit self-excited attractor and three different types of hidden attractors. Moreover, based on fractional-order finite time stability theory, we design finite time synchronization scheme of this new system. And combination synchronization of three fractional-order chaotic systems with hidden chaotic attractors is also derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization methods.
Hidden Chaotic Attractors and Synchronization for a New Fractional-Order Chaotic System
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 22, 2018; final manuscript received April 23, 2019; published online June 10, 2019. Assoc. Editor: Firdaus Udwadia.
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Wang, Z., Liu, J., Zhang, F., and Leng, S. (June 10, 2019). "Hidden Chaotic Attractors and Synchronization for a New Fractional-Order Chaotic System." ASME. J. Comput. Nonlinear Dynam. August 2019; 14(8): 081010. https://doi.org/10.1115/1.4043670
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