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research-article

Hidden chaotic attractors and synchronization for a new fraction-order chaotic system

[+] Author and Article Information
Zuoxun Wang

Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), No. 3501 Daxue Road, Jinan 250353, China
wangzuoxun@126.com

Jiaxun Liu

Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), No. 3501 Daxue Road, Jinan 250353, China
liujiaxunliujiaxun@163.com

Fangfang Zhang

Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), No. 3501 Daxue Road, Jinan 250353, China
zhff4u@163.com

Sen Leng

Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), No. 3501 Daxue Road, Jinan 250353, China
ls119@foxmail.com

1Corresponding author.

ASME doi:10.1115/1.4043670 History: Received December 22, 2018; Revised April 23, 2019

Abstract

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 firstly extend LE_1 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. Secondly, 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.

Copyright (c) 2019 by ASME
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