一个具有多翼吸引子的四维多稳态超混沌系统

鲜永菊1,扶坤荣1,徐昌彪1,2

振动与冲击 ›› 2021, Vol. 40 ›› Issue (1) : 15-22.

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (1) : 15-22.
论文

一个具有多翼吸引子的四维多稳态超混沌系统

  • 鲜永菊1,扶坤荣1,徐昌彪1,2
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A 4-D multi-stable hyper-chaotic system with multi-wing attractors

  • XIAN Yongju1, FU Kunrong1, XU Changbiao1,2
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摘要

构造了一个只有一个平衡点的四维超混沌系统,此系统表现出丰富的多稳态特性,亦具有多翼吸引子。数值分析了系统的动力学特性,仿真了系统的模拟电路和数字电路,探讨了系统的动态复杂度,测试了系统超混沌序列的随机性。分析结果表明,在多组参数值下,系统均存在不同类型的吸引子共存,譬如:两个周期吸引共存,周期与拟周期吸引子共存,双翼混沌与超混沌吸引子共存,两个双翼混沌吸引子共存,双翼与四翼混沌吸引子共存,两个双翼超混沌吸引子共存,两个双翼拟周期吸引子共存,两个双翼超混沌、四翼混沌、四翼超混沌等四个吸引子共存。系统的数字电路和模拟电路的仿真结果均与数值分析结果一致,表明了系统的可实现性。另外,在混沌和超混沌状态下系统复杂度高,且超混沌序列通过了SP800-22 Revla的15项随机测试。

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.

关键词

超混沌系统 / 多稳态性 / 多翼吸引子 / 电路仿真

Key words

hyper-chaotic system / multi-stability / multi-wing attractor / circuit simulation

引用本文

导出引用
鲜永菊1,扶坤荣1,徐昌彪1,2. 一个具有多翼吸引子的四维多稳态超混沌系统[J]. 振动与冲击, 2021, 40(1): 15-22
XIAN Yongju1, FU Kunrong1, XU Changbiao1,2. A 4-D multi-stable hyper-chaotic system with multi-wing attractors[J]. Journal of Vibration and Shock, 2021, 40(1): 15-22

参考文献

[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.

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