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Synchronization, anti-synchronization and circuit realization of a novel hyper-chaotic system

Yanjun Lu (Key Laboratory of Manufacturing Equipment of Shaanxi Province, Xi’an University of Technology, Xi’an, China)
Li Xiong (Key Laboratory of Manufacturing Equipment of Shaanxi Province, Xi’an University of Technology, Xi’an, China, and School of Physics and Electromechanical Engineering, Hexi University, Zhangye, China)
Yongfang Zhang (State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, China, and School of Printing, Packaging Engineering and Digital Media Technology, Xi’an University of Technology, Xi’an, China)
Peijin Zhang (CAS Key Laboratory of Geospace Environment, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, China)
Cheng Liu (Key Laboratory of Manufacturing Equipment of Shaanxi Province, Xi’an University of Technology, Xi’an, China)
Sha Li (Key Laboratory of Manufacturing Equipment of Shaanxi Province, Xi’an University of Technology, Xi’an, China)
Jianxiong Kang (Key Laboratory of Manufacturing Equipment of Shaanxi Province, Xi’an University of Technology, Xi’an, China)

Circuit World

ISSN: 0305-6120

Article publication date: 4 July 2018

Issue publication date: 16 July 2018

136

Abstract

Purpose

This paper aims to introduce a novel four-dimensional hyper-chaotic system with different hyper-chaotic attractors as certain parameters vary. The typical dynamical behaviors of the new hyper-chaotic system are discussed in detail. The control problem of these hyper-chaotic attractors is also investigated analytically and numerically. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components.

Design/methodology/approach

The adaptive control method is derived to achieve chaotic synchronization and anti-synchronization of the novel hyper-chaotic system with unknown parameters by making the synchronization and anti-synchronization error systems asymptotically stable at the origin based on Lyapunov stability theory. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components. Multisim simulations and electronic circuit experiments are consistent with MATLAB simulation results and they verify the existence of these hyper-chaotic attractors.

Findings

Comparisons among MATLAB simulations, Multisim simulation results and physical experimental results show that they are consistent with each other and demonstrate that changing attractors of the hyper-chaotic system exist.

Originality/value

The goal of this paper is to construct a new four-dimensional hyper-chaotic system with different attractors as certain parameters vary. The adaptive synchronization and anti-synchronization laws of the novel hyper-chaotic system are established based on Lyapunov stability theory. The corresponding electronic circuits for the novel hyper-chaotic system with different attractors are also implemented to illustrate the accuracy and efficiency of chaotic circuit design.

Keywords

Acknowledgements

Competing interests: The authors have declared that no competing interests exist.

Funding: The authors are greatly thankful for the help and support from the National Natural Science Foundation of China (Grant No. 51505375), Open Project of State Key Laboratory for Strength and Vibration of Mechanical Structures of China (Grant No. SV2016-KF-10), Research Program of Shaanxi Provincial Education Department of China (Grant No. 15JS068) and Shaanxi Provincial Natural Science Foundation of China (Grant No. 2014JM2-5082).

Citation

Lu, Y., Xiong, L., Zhang, Y., Zhang, P., Liu, C., Li, S. and Kang, J. (2018), "Synchronization, anti-synchronization and circuit realization of a novel hyper-chaotic system", Circuit World, Vol. 44 No. 3, pp. 132-149. https://doi.org/10.1108/CW-01-2018-0005

Publisher

:

Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

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