Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

doi:10.1088/1674-1056/26/11/110502

中国物理B ›› 2017, Vol. 26 ›› Issue (11): 110502-110502.doi: 10.1088/1674-1056/26/11/110502

Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

Xiaoyu Hu(胡晓宇), Chongxin Liu(刘崇新), Ling Liu(刘凌), Yapeng Yao(姚亚鹏), Guangchao Zheng(郑广超)

State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China

收稿日期:2017-04-24 修回日期:2017-08-01 出版日期:2017-11-05 发布日期:2017-11-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 51177117 and 51307130).

Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

Xiaoyu Hu(胡晓宇), Chongxin Liu(刘崇新), Ling Liu(刘凌), Yapeng Yao(姚亚鹏), Guangchao Zheng(郑广超)

State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China

Received:2017-04-24 Revised:2017-08-01 Online:2017-11-05 Published:2017-11-05
Contact: Xiaoyu Hu E-mail:huxiaoyucool@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 51177117 and 51307130).

摘要/Abstract

摘要： A novel 5-dimensional (5D) memristive chaotic system is proposed, in which multi-scroll hidden attractors and multi-wing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincaré map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.

关键词: multi-scroll hidden attractors, multi-wing hidden attractors, multiple lines equilibria, no equilibrium

Abstract: A novel 5-dimensional (5D) memristive chaotic system is proposed, in which multi-scroll hidden attractors and multi-wing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincaré map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.

Key words: multi-scroll hidden attractors, multi-wing hidden attractors, multiple lines equilibria, no equilibrium

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Jn (High-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)

胡晓宇, 刘崇新, 刘凌, 姚亚鹏, 郑广超. Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system[J]. 中国物理B, 2017, 26(11): 110502-110502.

Xiaoyu Hu(胡晓宇), Chongxin Liu(刘崇新), Ling Liu(刘凌), Yapeng Yao(姚亚鹏), Guangchao Zheng(郑广超). Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system[J]. Chin. Phys. B, 2017, 26(11): 110502-110502.

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Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

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