基于可调宽度的多涡卷保守混沌系统的构建

doi:10.16088/j.issn.1001-6600.2024041605

Abstract

Abstract: Compared with dissipative multi-scroll chaotic systems, conservative multi-scroll chaotic systems exhibit potential application prospects in image encryption and secure communication, rendering the research significantly meaningful. Based on the principle of Hamiltonian energy conservation, a four-dimensional conservative chaotic system is constructed in this peper. By introducing piecewise functions, the equilibrium points of the system are expanded, resulting in a multi-scroll chaotic system with adjustable widths along the x and y directions. By adjusting the system parameters and initial values, multi-scroll-like attractors with different energy levels and scroll numbers are generated. Notably, as the number of scrolls increases, the Lyapunov exponent of the system also exhibits a gradually increasing trend. Through NIST testing, the potential value of the system in applications such as random signal generators and image encryption is verified. Experimental results show that the SE value of the system reaches 0.63, fully demonstrating its practicality and importance in the field of secure communication.

Key words: chaotic system, Lyapunov exponent, NIST test, random signal generator, image encryption

CLC Number: O415.5

YAN Minxiu, ZHAO Qi. Dynamic Analysis Multi-scroll Conservative Chaotic Systems Based on Controllable Width[J].Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(2): 42-55.

References

[1] LORENZ E N. Deterministic nonperiodic flow[J]. Journal of the Atmospheric Sciences, 1963, 20(2): 130-141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
[2] 张泽峰,黄丽莲,项建弘,等.新的具有宽参数范围的五维保守超混沌系统的动力学研究[J].物理学报,2021,70(23):128-138.DOI: 10.7498/aps.70.20210592.
[3] 颜闽秀,朱君洋.含大范围参数四维混沌系统的吸引子共存[J].深圳大学学报(理工版),2024,41(1):108-117.DOI: 10.3724/SP.J.1249.2024.01108.
[4] 邵慧婷,杨启贵.具有4个正Lyapunov指数的六维超混沌系统的复杂动力学研究[J].广西师范大学学报(自然科学版),2022,40(5):433-444.DOI: 10.16088/j.issn.1001-6600.2020022803.
[5] LAI Q, YANG L, LIU Y. Design and realization of discrete memristive hyperchaotic map with application in image encryption[J]. Chaos Solitons & Fractals, 2022, 165(Part 1): 112781. DOI: 10.1016/j.chaos.2022.112781.
[6] 梁钰婷,罗玉玲,张顺生.基于压缩感知的混沌图像加密研究综述[J].广西师范大学学报(自然科学版),2022,40(5):49-58.DOI: 10.16088/j.issn.1001-6600.2022012003.
[7] 李蓝航,丘森辉,肖丁维,等.基于DNA序列和动态索引扩散的图像加密算法[J].广西师范大学学报(自然科学版),2021,39(3):40-53.DOI: 10.16088/j.issn.1001-6600.2020080503.
[8] ZHENG P S, TANG W S, ZHANG J X. Some novel double-scroll chaotic attractors in Hopfield networks[J]. Neurocomputing, 2010, 73(10/12): 2280-2285. DOI: 10.1016/j.neucom.2010.02.015.
[9] MA C G, MOU J, YANG F F, et al. A fractional-order Hopfield neural network chaotic system and its circuit realization[J]. The European Physical Journal Plus, 2020, 135(1): 100. DOI: 10.1140/epjp/s13360-019-00076-1.
[10] CHUA L. Everything you wish to know about memristors but are afraid to ask[M] // CHUA L, SIRAKOULIS G C, ADAMATZKY A. Handbook of Memristor Networks. Cham: Springer, 2019: 89-157. DOI: 10.1007/978-3-319-76375-0_3.
[11] LIN H R, WANG C H, SUN Y C, et al. Firingmultistability in a locally active memristive neuron model[J]. Nonlinear Dynamics, 2020, 100(4): 3667-3683. DOI: 10.1007/s11071-020-05687-3.
[12] BAO B C, QIAN H, XU Q, et al. Coexisting behaviors of asymmetric attractors in hyperbolic-type memristor based Hopfield neural network[J]. Frontiers in Computational Neuroscience, 2017, 11: 81. DOI: 10.3389/fncom.2017.00081.
[13] LI R H, WANG Z H, DONG E Z. A new locally active memristive synapse-coupled neuron model[J]. Nonlinear Dynamics, 2021, 104(4): 4459-4475. DOI: 10.1007/s11071-021-06574-1.
[14] CHENG G H, LI D, YAO Y G, et al. Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells[J]. Chaos, Solitons, and Fractals, 2023, 174: 113837. DOI: 10.1016/j.chaos.2023.113837.
[15] LIN H R, WANG C H, YU F, et al. A triple-memristor Hopfield neural network with space multistructure attractors and space initial-offset behaviors[J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2023, 42(12): 4948-4958. DOI: 10.1109/TCAD.2023.3287760.
[16] ZHAO M Y, YANG Q G, ZHANG X. Dynamics of a class of Chua’s oscillator with a smooth periodic nonlinearity: Occurrence of infinitely many attractors[J]. Communications in Nonlinear Science and Numerical Simulation, 2022, 115: 106744. DOI: 10.1016/j.cnsns.2022.106744.
[17] LIU X L, TONG X J, WANG Z, et al. Construction of controlled multi-scroll conservative chaotic system and its application in color image encryption[J]. Nonlinear Dynamics, 2022, 110(2): 1897-1934. DOI: 10.1007/s11071-022-07702-1.
[18] DONG E Z, LI R H, DU S Z. A multi-directional controllable multi-scroll conservative chaos generator: Modelling, analysis, and FPGA implementation[J]. Chinese Physics B, 2021, 30(2): 020505. DOI: 10.1088/1674-1056/abc239.
[19] YANG Y, HUANG LL, XIANG J H, et al. Three-dimensional sine chaotic system with multistability and multi-scroll attractor[J]. IEEE Transactions on Circuits and Systems II-Express Briefs, 2022, 69(3): 1792-1796. DOI: 10.1109/TCSII.2021.3126227.
[20] LIU J W, CHEN Z G. A generalized Hamiltonian conservative system with multi-scroll chaotic flows[C] // The 2022 International Conference on Artificial Life and Robotics. Oita: ALife Robotics Corporation Ltd., 2022: 132-136. DOI: 10.5954/ICAROB.2022.OS33-3.
[21] LIN H R, WANG C H, SUN Y C. A universal variable extension method for designingmultiscroll/wing chaotic systems[J]. IEEE Transactions on Industrial Electronics, 2024, 71(7): 7806-7818. DOI: 10.1109/TIE.2023.3299020.
[22] LIN H R, WANG C H, SUN Y C, et al. Generatingn-scroll chaotic attractors from a memristor-based magnetized Hopfield neural network[J]. IEEE Transactions on Circuits and Systems II-Express Briefs, 2023, 70(1): 311-315. DOI: 10.1109/tcsii.2022.3212394.
[23] LIN H R, WANG C H, DU S C, et al. A family ofmemristive multibutterfly chaotic systems with multidirectional initial-based offset boosting[J]. Chaos, Solitons, and Fractals, 2023, 172: 113518. DOI: 10.1016/j.chaos.2023.113518.
[24] NAIK R B, SINGH U. A review on applications of chaotic maps in pseudo-random number generators and encryption[J]. Annals of Data Science, 2024, 11(1): 25-50. DOI: 10.1007/s40745-021-00364-7.
[25] DEHGHANI R, KHEIRI H. Chaotic-based color image encryption using a hybrid method of reversible cellular automata and DNA sequences[J]. Multimedia Tools and Applications, 2024, 83(6): 17429-17450. DOI: 10.1007/s11042-023-16118-x.
[26] DENG Q L, WANG C H. Multi-scroll hidden attractors with two stable equilibrium points[J]. Chaos, 2019, 29(9): 093112. DOI: 10.1063/1.5116732.
[27] RAJAGOPAL K, ÇIÇEK S, NASERADINMOUSAVI P, et al. A novel parametrically controlled multi-scroll chaotic attractor along with electronic circuit design[J]. The European Physical Journal Plus, 2018,133(9): 354. DOI: 10.1140/epjp/i2018-12168-9.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 0

No Suggested Reading articles found!

Dynamic Analysis Multi-scroll Conservative Chaotic Systems Based on Controllable Width

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 8

Metrics

Comments

Recommended 0

[1]	YAN Minxiu, JIN Qisen. Construction of Multi-dimensional Chaotic Systems and Its Multi-channel Adaptive Control [J]. Journal of Guangxi Normal University(Natural Science Edition), 2023, 41(6): 8-21.
[2]	LIANG Yuting, LUO Yuling, ZHANG Shunsheng. Review on Chaotic Image Encryption Based on Compressed Sensing [J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(5): 49-58.
[3]	SHAO Huiting, YANG Qigui. Complex Dynamics of a Six-dimensional Hyperchaotic System with Four Positive Lyapunov Exponents [J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(5): 433-444.
[4]	LI Lanhang, QIU Senhui, WANG Wenyi, XIAO Dingwei, LUO Yuling. Multi-layer Interactive Color Image Encryption Algorithm Based on Chaotic Map [J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(6): 72-86.
[5]	LI Songtao, LI Qunhong, ZHANG Wen. Co-dimension-two Grazing Bifurcation and Chaos Control of Three-degree-of-freedom Vibro-impact Systems [J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(4): 79-92.
[6]	LI Lanhang, QIU Senhui, XIAO Dingwei, LI Liangjia, OUYANG Xue, LUO Yuling. Image Encryption Algorithm Based on DNA Sequence and Dynamic Index Diffusion [J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(3): 40-53.
[7]	HONG Lingling, YANG Qigui. Research on Complex Dynamics of a New 4D Hyperchaotic System [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(3): 96-105.
[8]	YANG Kun, LIN Jiao, JIANG Gui-rong. Dynamics Analysis of a Stochastic SIS Epidemic Model with Birth Pulses [J]. Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(4): 81-86.