A Novel Four-Dimensional No-Equilibrium Hyper-Chaotic System With Grid Multiwing Hyper-Chaotic Hidden Attractors

[+] Author and Article Information
Sen Zhang

School of Physics and Opotoelectric
Xiangtan University,
Xiangtan 411105, Hunan, China
e-mail: 18337193139@163.com

Yi Cheng Zeng

School of Physics and Opotoelectric
Xiangtan University,
Xiangtan 411105, Hunan, China
e-mail: yichengz@xtu.edu.cn

Zhi Jun Li

College of Information Engineering,
Xiangtan University,
Xiangtan 411105, Hunan, China
e-mail: lizhijun_320@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 15, 2017; final manuscript received April 7, 2018; published online July 26, 2018. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 13(9), 090908 (Jul 26, 2018) (9 pages) Paper No: CND-17-1267; doi: 10.1115/1.4039980 History: Received June 15, 2017; Revised April 07, 2018

By using a simple state feedback control technique and introducing two new nonlinear functions into a modified Sprott B system, a novel four-dimensional (4D) no-equilibrium hyper-chaotic system with grid multiwing hyper-chaotic hidden attractors is proposed in this paper. One remarkable feature of the new presented system is that it has no equilibrium points and therefore, Shil'nikov theorem is not suitable to demonstrate the existence of chaos for lacking of hetero-clinic or homo-clinic trajectory. But grid multiwing hyper-chaotic hidden attractors can be obtained from this new system. The complex hidden dynamic behaviors of this system are analyzed by phase portraits, the time domain waveform, Lyapunov exponent spectra, and the Kaplan–York dimension. In particular, the Lyapunov exponent spectra are investigated in detail. Interestingly, when changing the newly introduced nonlinear functions of the new hyper-chaotic system, the number of wings increases. And with the number of wings increasing, the region of the hyper-chaos is getting larger, which proves that this novel proposed hyper-chaotic system has very rich and complicated hidden dynamic properties. Furthermore, a corresponding improved module-based electronic circuit is designed and simulated via multisim software. Finally, the obtained experimental results are presented, which are in agreement with the numerical simulations of the same system on the matlab platform.

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Grahic Jump Location
Fig. 1

Double-wing hidden attractors of system (1): (a) zy plane and (b) xy plane

Grahic Jump Location
Fig. 2

The Lyapunov exponents of system (1) with b varying

Grahic Jump Location
Fig. 3

The nonlinear function waveforms: (a) P(z) with N = 1 and (b) Q(y) with M = 1

Grahic Jump Location
Fig. 4

Grid multiwing hyper-chaotic hidden attractors in zy and xy plane: (a) 4×2−wing attractor, (b) 6×2−wing attractor, (c) 4×4−wing attractor, and (d) 6×4−wing attractor

Grahic Jump Location
Fig. 5

Time responses of the third state variable of the grid multiwing hyper-chaotic hidden attractors: (a) 4×2−wing attractor, (b) 6×2−wing attractor, (c) 4×4−wing attractor, and (d) 6×4−wing attractor

Grahic Jump Location
Fig. 6

The Lyapunov exponents spectra of different number of wings with b varying: (a) 4×2−wing attractor, (b) 6×2−wing attractor, (c) 4×4−wing attractor, and (d) 6×4−wing attractor

Grahic Jump Location
Fig. 7

Circuit implementation of the new system (6)

Grahic Jump Location
Fig. 8

Circuits implementation of the new nonlinear functions: (a) P(z) and (b) Q(y)

Grahic Jump Location
Fig. 9

Experimental results of the grid multiwing hyper-chaotic hidden attractors in zy and xy plane: (a) 4×2−wing attractor, (b) 6×2−wing attractor, (c) 4×4−wing attractor, and (d) 6×4−wing attractor



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