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Special Characteristics and Synchronizations of Multi Hybrid-Order Chaotic Systems

1
School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
2
Shandong Computer Science Center (National Supercomputer Center in Jinan), Shandong Artificial Intelligence Institute, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250101, China
3
College of Control Science and Engineering, Shandong University, Jinan 250061, China
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(6), 664; https://doi.org/10.3390/e22060664
Received: 22 May 2020 / Revised: 11 June 2020 / Accepted: 11 June 2020 / Published: 16 June 2020
Based on advantages of integer and fractional chaotic systems, hybrid chaotic systems and their definitions and some fundamental concepts are proposed, such as hybrid degree (HD), the lowest order (LO) and the total dimension order (TDO). The preliminary properties of hybrid Lorenz systems and hybrid forms of some classic chaotic systems are studied. Then, the relations between HD, LO and TDO with different parameters is investigated in chaotic systems. To be specific, HD is associated with fractional order. It is a directional method to search LO and TDO in chaotic systems. Finally, based on the incommensurate fractional stability theory, we accomplish combination synchronization for three different hybrid order chaotic systems. The simulation results verify the effectiveness of the synchronization controller. View Full-Text
Keywords: hybrid order chaotic systems; fractional order; hybrid degree; combination synchronization hybrid order chaotic systems; fractional order; hybrid degree; combination synchronization
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Liu, J.; Wang, Z.; Zhang, F.; Yin, Y.; Ma, F. Special Characteristics and Synchronizations of Multi Hybrid-Order Chaotic Systems. Entropy 2020, 22, 664.

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