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由于忆阻器具有独特的非线性特性和记忆效应,基于忆阻器的混沌系统成为目前研究的热点.然而,关于忆阻混沌系统的不稳定周期轨道研究目前较少.本文通过引入三角函数忆阻器改进三维混沌系统,构建了一个新型四维忆阻混沌系统.通过Lyapunov指数、庞加莱截面、相图、时域波动图对系统进行动力学行为分析.针对变分法在寻找可靠圈猜想受限的问题,创新性地提出了一种基于三角函数物理特性的优化策略.通过该优化策略,结合符号动力学对新系统的不稳定周期轨道进行了系统分析,并进一步采用自适应反步法控制已知轨道的稳定性.对新型忆阻混沌系统序列进行NIST测试,发现该序列具有良好的伪随机性,适用于图像加密算法的应用.设计了基于新系统的图像加密算法,忆阻混沌系统的应用显著提高了密钥空间和密钥敏感度,增强了图像加密的安全性.算法首先通过RGB三个通道之间的跨平面置乱对彩色图像像素首次置乱,随后进行单平面的二次置乱,充分改变图像像素.算法采用异或运算进行扩散,其NPCR和UACI的平均值表明其具有强大的差分攻击能力.此外,通过直方图、相关性、抗剪切攻击及运行时间等测试验证其可靠性.最后,在DPS平台上验证了实验结果与数值分析结果的一致性.Due to their unique nonlinear characteristics and memory effects, memristor-based chaotic systems have become a significant focus of research. However, studies on unstable periodic orbits in memristive chaotic systems remain relatively scarce. In this paper, a novel four-dimensional memristive chaotic system is constructed by introducing a trigonometric-function-based memristor to enhance a three-dimensional chaotic system. The dynamical behaviors of the system are analyzed using Lyapunov exponents, Poincaré sections, phase portraits, and time-domain plots. The proposed memristive chaotic system exhibits rich dynamical characteristics, including transient behavior, intermittent chaos, and diverse attractor dynamics under parameter variations. To overcome the limitations of the variational method in finding reliable initial guesses for unstable periodic orbits, an innovative optimization strategy leveraging the physical characteristics of trigonometric functions is proposed. Integrated with symbolic dynamics, this strategy enables the rapid acquisition of robust initial guesses for unstable periodic orbits within specific intervals. Furthermore, it allows for the migration of these guesses to other regions of the attractor, ultimately achieving full coverage of the attractor's unstable periodic orbits. Following a systematic analysis of the unstable periodic orbits in the new system, the adaptive backstepping method is employed to control the stability of the known unstable periodic orbits, namely 320 and 013. The pseudorandom sequences generated by the novel memristive chaotic system successfully passed the NIST suite, with all test items yielding P-values greater than 0.01, which confirms their excellent pseudo-random characteristics. The application of this system in image encryption achieves a key space of 10120, significantly enhancing the key space and key sensitivity of the algorithm. The encryption process begins with cross-plane scrambling operations among the RGB color channels for initial pixel processing, followed by intra-plane scrambling to further disrupt the pixel arrangement. XOR operations are then employed for pixel value diffusion. The algorithm demonstrates outstanding resistance to differential attacks, with average NPCR and UACI values reaching 99.6041% and 33.4933%, respectively. Comprehensive security analyses, including histogram analysis, correlation analysis, resistance to cropping attacks, and runtime evaluation, verify that the proposed encryption scheme not only possesses strong security capabilities but also maintains high computational efficiency, making it highly suitable for practical image encryption applications. Finally, the realizability of the system is verified by utilizing a DSP circuit.
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Keywords:
- Chaotic System /
- Memristor /
- Periodic Orbit /
- Image Encryption
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[1] Sella Y, Broderick N A, Stouffer K M, McEwan D L, Ausubel F M, Casadevall A, Bergman A 2024 Msystems. 9 23 01110
[2] Han Z T, Sun B, Banerjee S, Mou J 2024 Chaos Solitons Fract. 184 115020
[3] Xu Q, Ding X C, Wang N, Chen B, Parastesh F, Chen M 2024 Chaos Solitons Fract. 187 115339
[4] Murphy K A, Bassett D S 2017 Phys. Rev. Lett. 132 197201
[5] X Yan, Q Hu, L Teng, Y Su 2024 Chaos Solitons Fract. 185 115146
[6] Vogl M 2024 Commun Nonlinear Sci. 130 107760
[7] Rehman Z U, Boulaaras S, Jan R, Ahmad I, Bahramand S 2024 J Comput Sci. 75 102204
[8] Li L. 2024 Expert Syst. Appl. 252 124316
[9] Umar T, Nadeem M, Anwer F. 2004 Expert Syst. Appl. 257 125050
[10] Wang C H, Tang D, Lin H, Yu F, Sun Y C 2024 Expert Syst. Appl. 242 122513
[11] Leonov G, Kuznetsov N 2013 Int. J. Bifur. Chaos 23 1330002
[12] Dong C W, Yang M 2024 Chin. J. Phys. 89 930
[13] Dong C W, Yang M, Jia L, Li Z R 2024 Phys. A 633 129391
[14] Wei D S, Dong C W 2024 Phys. Scr 99 085251
[15] Dong C W 2022 Fractal Fract. 6 547
[16] Dong C W, Yang M 2024 Fractal Fract. 8 266
[17] Dong C W, Iu H H C 2025 Chin. J. Phys. 97 433
[18] Wang P J, Wu G Z. 2005 Acta Phys. Sin. 54 3034 (in Chinese)[王培杰，吴国珍2005 物理学报 54 3034]
[19] Sanchez J, Net M. 2010 Int. J. Bifur. Chaos 20 43
[20] Lan Y, Cvitanović P 2004 Phys. Rev. E 69 016217
[21] Dong C W 2018 Acta Phys. Sin. 76 55 (in Chinese) [董成伟 2018 物理学报 76 55]
[22] Chua L O 1971 IEEE Trans. Circuits Theor. 18 507
[23] Strukov D B,Snider G S, Stewart D R, Stanley W R 2008 Nature 453 80
[24] Xiao Y Y, Jiang B, Zhang Z, Ke S W, Jin Y Y, Wen X, Ye C. 2023 Sci. Technol. Adv. Mater. 24 2162323
[25] Zhang L, Li Z, Peng Y 2024 Chaos Solitons Fract. 185 115109
[26] Diao Y F, Huang S F, Huang L Q, Xiong X M, Yang J, Cai S T 2024 Chaos Solitons Fract. 188 115526
[27] An X L, Liu S Y, Xiong L, Zhang J G, Li XY 2024 Expert Syst. Appl. 243 122899
[28] Kong X, Yu F, Yao W, Cai S, Zhang J, Lin H 2024 Neural Netw. 171 85
[29] He S, Hu K, Wang M, Wang H, Wu X 2024 Chaos Solitons Fract. 188 115517
[30] Lai Q,Wang J 2024 Acta Phys. Sin. 73 75(in Chinese) [赖强, 王君 2024 物理学报 73 75]
[31] Njitacke Z T, Takembo C N, Awrejcewicz J, Fouda H P E, Kengne J 2022 Chaos Solitons Fract. 160 112211
[32] Zhang X, Xu J, Moshayedi A J 2024 Chaos Solitons Fract. 179 114460
[33] Lampartová A, Lampart M 2024 Chaos Solitons Fract. 182 114863
[34] Wu H G, Ban Y X, Chen M, Chen Q 2024 J.Electron.Inf.Techn. 46 3818 (in Chinese) [武花干, 边逸轩, 陈墨, 徐权 2024 电子与信息学报 46 3818]
[35] Hua C C, Guan X P 2004 Chaos Solitons Fract. 22 55
[36] Konishi K, Hirai M, Kokame H 1998 Phys.Lett.A. 245 511
[37] Dadras S,Momeni H R 2009 Chaos Solitons Fract. 42 3140
[38] Rasappan S,Vaidyanathan S 2014 Kyungpook Math. J. 54 293
[39] Pan Y, Ji W, Liang H 2022 IEEE Trans. Circuits Syst. II-Express Briefs. 69 5064
[40] Zhang X, Yang X, Huang C, Cao J, Liu H 2024 Inf Sci 661 120148
[41] Wang Z, Li Y X, Hui X J,Lu L 2011 Acta Phys. Sin. 60 125(in Chinese) [王震, 李永新, 惠小健, 吕雷 2011 物理学报 60 125]
[42] Wu F, Wang G, Zhuang S, Wang K, Keimer A, Stoica I, Bayen A 2023 IEEE Trans. Autom. Sci. Eng. 21 2088
[43] Lin T C, Kuo C H 2012 Int. J. Syst. Dyn. Appl. 1 1
[44] Li X J, Sun B, Bi X G, Yan H Z, Wang L 2024 Mobile. Netw. Appl 29 583
[45] Chen J X, Zhu Z L, Zhang L B, Zhang Y S, Yang B Q 2017 Signal Process. 142 340
[46] Wang L N, Zhou N R, Sun B, Cao Y H 2024 Chin. Phys.B 33 050501
[47] Dehghani R, Kheiri H 2024 Multimed Tools Appl. 83 17429
[48] Xin J, Hu H, Zheng J 2023 Nonlinear Dyn.111 7859
[49] Wang Q, Zhang X, Zhao X 2023 Nonlinear Dyn. 111 22679
[50] Xiao W, Xuemei X, Kehui S, Zhaohui J, Mingjun L, Jun W 2023 Nonlinear Dyn.111 14513
[51] Zhang Z Y, Cao Y H, Zhou N R, Xu X Y, Mou J 2025 Appl. Intell. 55 61
[52] Cao H L, Cao Y H, Qin L, Mou J 2025 Chaos Solitons Fract. 191 115857
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