|
|
|
| A 4-D multi-stable hyper-chaotic system with multi-wing attractors |
| XIAN Yongju1, FU Kunrong1, XU Changbiao1,2 |
1.School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065,
China;
2.School of Optoelectronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China |
|
|
|
Abstract Here, a 4-D hyper-chaotic system with only one equilibrium point was constructed to reveal rich multi-stable characteristics with multi-wing attractors. The system’s dynamic characteristics were numerically analyzed, and the system’s analog circuit and digital circuit were simulated to explore the dynamic complexity of the system, and test the randomness of the system’s hyper-chaotic sequences. The analysis results showed that under multi-set of system parameters, there are coexistences of different types attractors in the system, such as, coexistence of two periodic attractors, coexistence of a periodic one and a quasi-periodic one, coexistence of a dual-wing chaotic one and a hyper-chaotic one, coexistence of two dual-wing chaotic ones, coexistence of a dual-wing chaotic one and a four-wing chaotic one, coexistence of two dual-wing hyper-chaotic ones, coexistence of two dual-wing quasi-periodic ones, coexistence of four attractors including two dual-wing hyper-chaotic ones, a four-wing chaotic one and a four-wing hyper-chaotic one; the simulation results of the system’s digital circuit and analog circuit are consistent to numerical analysis ones to reveal the system’s realizability; the system has high complexity in chaotic state and hyper-chaotic one, and its hyper-chaotic sequences pass 15 random tests specified in SP800-22 Revla.
|
|
Received: 10 April 2019
Published: 15 January 2021
|
|
|
|
[1] Tarasova V V, Tarasov V E. Logistic map with memory from economic model[J]. Chaos, Solitons & Fractals, 2017, 95(1):84-91.
[2] 牛治东, 吴光强. 电动汽车混沌振动信号的小波神经网络预测[J]. 振动与冲击, 2018, 37(8): 120-124.
Niu Zhidong, Wu Guangqiang. Wavelet neural network prediction of electric vehicle chaotic vibration signals[J]. Journal of Vibration and Shock, 2018, 37(8): 120-124.
[3] 李国正, 谭南林, 苏树强, 张驰. 基于Lorenz混沌同步系统的未知频率微弱信号检测[J]. 振动与冲击, 2019, 38(5): 155-161.
Li Guozheng, Tan Nanlin, Su Shuqiang, Zhang Chi. Unknown frequency weak signal detection based on Lorenz chaotic synchronization system[J]. Journal of Vibration and Shock, 2019, 38(5): 155-161.
[4] Vaidyanathan S, Akgul A, KaAr S, et al. A new 4-D chaotic hyperjerk system, its synchronization, circuit design and applications in RNG, image encryption and chaos-based steganography[J]. The European Physical Journal Plus, 2018, 133(2):46-50.
[5] Yudi F, Mengfan C, Xingxing J, et al. Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism[J]. Nonlinear Dynamics, 2018, 94(3):1949-1959.
[6] Li C, Sprott J C, Hu W, et al. Infinite Multistability in a Self-Reproducing Chaotic System[J]. International Journal of Bifurcation and Chaos, 2017, 27(10):1750160.
[7] Guan Z H, Hu B, Shen X. Multistability of Delayed Hybrid Impulsive Neural Networks[M]. 2019.
[8] Yong-Ju X, Cheng X, Tao-Tao G, et al. Dynamical analysis and FPGA implementation of a large range chaotic system with coexisting attractors[J]. Results in Physics, 2018, 11:368-376.
[9] Wang Z, Ma J, Cang S, et al. Simplified hyper-chaotic systems generating multi-wing non-equilibrium attractors[J]. Optik - International Journal for Light and Electron Optics, 2016, 127(5):2424-2431.
[10] Jay Prakash Singh1, Binoy Krishna Roy, and Zhouchao Wei. A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control[J]. Chin. Phys. B, 2018, 27(4): 214-227.
[11] Zhou Ling, Wang Chunhua, Zhou Lili. Generating four-wing hyperchaotic attractor and two-wing, three-wing, and four-wing chaotic attractors in 4-D memristive system[J]. International Journal of Bifurcation and Chaos, 2017, 27(02): 1750027.
[12] Zhou Chenyi, Li Zhijun, Zeng Yicheng, et al. A Novel 3-D Fractional-Order Chaotic System with Multifarious Coexisting Attractors[J]. International Journal of Bifurcation and Chaos, 2019, 29(1): 1950004.
[13] Borah M, Roy B K. An enhanced multi-wing fractional-order chaotic system with coexisting attractors and switching hybrid synchronisation with its nonautonomous counterpart[J]. Chaos, Solitons & Fractals, 2017, 102: 372-386.
[14] Wang G, Yuan F, Chen G, et al. Coexisting multiple attractors and riddled basins of a memristive system[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018, 28(1):125-130.
[15] Njitacke Z T, Kengne J, Negou A N. Dynamical analysis and electronic circuit realization of an equilibrium free 3D chaotic system with a large number of coexisting attractors[J]. Optik - International Journal for Light and Electron Optics, 2017, 1(1):130-139.
[16] Zhang Chaoxia. Theoretical design approach of four-dimensional piecewise-linear multi-wing hyperchaotic differential dynamic system[J]. Optik - International Journal for Light and Electron Optics, 2016, 127(11):4575-4580.
[17] Lai Q, Akgul A, Zhao X W, et al. Various types of coexisting attractors in a new 4-D autonomous chaotic system[J]. International Journal of Bifurcation and Chaos, 2017, 27(09):142-150.
[18] Zhang Sen, Zeng Yicheng, Li Zhijun, et al. Generating one to four-wing hidden attractors in a novel 4-D no-equilibrium chaotic system with extreme multistability[J]. Chaos, 2018, 28(1): 013113.
[19] 孙克辉. 混沌保密通信原理与技术[M]. 清华大学出版社, 2015.
Sun Kehui. Principle and technology of chaotic secure communication[M]. Tsinghua University Press, 2015.
[20] 张勇. 混沌数字图像加密[M]. 清华大学出版社, 2016.
Zhang Y. Chaotic Digital Image Cryptosystem[M]. Tsinghua University Press, 2016.
|
|
|
|
