A New Chaotic System Analysis and Synchronization Control
ZHOU Qunli1,2, SONG Quanjun2, PAN Hongqing2,3
1. Institute of Electrical and Automation, Wuhu Vocational Technical University, Wuhu 241006, China; 2. Hefei Institute of Intelligent Machines, Chinese Academy of Science, Hefei 230031, China; 3. Anhui Ganba Electric Appliance Co, Ltd, Hefei 230088, China
Abstract：In order to enrich the chaotic system model, a four-dimensional hyperchaotic system is constructed based on the Chen chaotic system. By analyzing the dissipation, equilibrium points, stability, sensitivity to initial values, bifurcation diagram, Lyapunov exponent spectra, LE dimension, power spectra and poincaré mapping of the new chaotic system, the rich and complex dynamic characteristics of the new chaotic system are revealed. In order to further enhance the security of information in secure communication, the new chaotic system and Qi hyperchaotic system are synchronized by using the transform modified function projective synchronization method, and a synchronization controller is designed to realize fast synchronization between hyperchaotic systems with different structures. The theoretical analysis and simulation results are consistent. Compared with the adaptive synchronous controller, the time required for the drive system and the response system to achieve synchronization is obviously shortened, which reflects the superiority of the method proposed in this paper.
周群利, 宋全军, 潘宏青. 一个新的混沌系统分析及同步控制[J]. 复杂系统与复杂性科学, 2025, 22(3): 82-89.
ZHOU Qunli, SONG Quanjun, PAN Hongqing. A New Chaotic System Analysis and Synchronization Control[J]. Complex Systems and Complexity Science, 2025, 22(3): 82-89.
[1] LORENZ E N. Deterministic nonperiodic flow[J]. Journal of the Atmospheric Sciences, 1963, 20(2): 130-141. [2] CHEN G R, UETA T. Yet another chaotic attractor[J]. International Journal of Bifurcation and Chaos, 1999, 9(7): 1465-1466. [3] LU J H, CHEN G R. A new chaotic attractor coined[J]. International Journal of Bifurcation and Chaos, 2002, 12(3): 659-661. [4] ZHAO H Y, WANG S S, WANG X Y. Fast image encryption algorithm based on multi-parameter fractal matrix and MPMCML system[J]. Chaos Solitons and Fractals, 2022, 164: 112742. [5] 时帅帅, 刘立才, 杜传红. 新混沌系统分析及其同步控制[J]. 工程数学学报, 2022, 39(5): 709-724. SHI S S, LIU L C, DU C H. Analysis and synchronization control of new chaotic systems[J]. Chinese Journal of Engineering Mathematics, 2022, 39(5):709-724. [6] 闫少辉, 顾斌贤, 宋震龙, 等. 基于一种四维忆阻超混沌系统的图像加密算法[J]. 复杂系统与复杂性科学, 2023, 20(2): 43-51. YAN S H, GU B X, SONG Z L, et al. Image encryption algorithm based on a four-dimensional memristor hyperchaotic system[J]. Complex Systems and Complexity Science, 2023, 20(2): 43-51. [7] Al-KHASAWNEH M A, UDDIN I, SHAH S A A, et al. An improved chaotic image encryption algorithm using Hadoop-based MapReduce framework for massive remote sensed images in parallel IoT applications[J]. Cluster Computing, 2022, 25(2): 999-1013. [8] 禹思敏, 吕金虎, 李澄清. 混沌密码及其在多媒体保密通信中应用的进展[J]. 电子与信息学报, 2016, 38(3): 735-752. YU S M, LÜ J H, LI C Q. Some progresses of chaotic cipher and its applications in multimedia secure communications[J]. Journal of Electronics & Information Technology, 2016, 38(3): 735-752. [9] LUO Y Q, YU J, LAI W R, et al. A novel chaotic image encryption algorithm based on improved baker map and logistic map[J]. Multimedia Tools and Applications, 2019, 78(15): 22023-22043. [10] MAY R M. Simple mathematical models with very complicated dynamics[J]. The Theory of Chaotic Attractors, 2004(1): 85-93. [11] 吴雅文. 混沌系统动力学分析与同步问题研究[D]. 南京: 南京信息工程大学,2021. WU Y W. Dynamics analysis and synchronization of chaotic systems[D]. Nanjing: Nanjing University of Information Science and Technology, 2021. [12] 李正峰. 几类特殊复超混沌系统及其同步控制[D].济南: 齐鲁工业大学,2022. LI Z F. Several special hyperchaotic complex systems and their synchronization control[D]. Jinan: Qilu University of Technology, 2022. [13] 刘泉, 李佩玥, 章明朝, 等. 基于可Markov分割混沌系统的图像加密算法[J]. 电子与信息学报, 2014, 36(6): 1271-1277. LIU Q, LI P Y, ZHANG M C, et al. Image encryption algorithm based on chaos system having Markov portion[J]. Journal of Electronics & Information Technology, 2014, 36(6): 1271-1277. [14] 文昌辞, 王沁, 黄付敏, 等. 基于仿射和复合混沌的图像自适应加密算法[J]. 通信学报, 2012, 33(11): 119-127. WEN C C, WANG Q, HUANG F M, et al. Selfadaptive encryption algorithm for image based on affine and composed chaos[J]. Journal on Communications, 2012, 33(11): 119-127. [15] 葛辛, 刘粉林, 芦斌, 等. 基于搜索机制混沌加密算法的密文特性分析[J]. 电子与信息学报, 2008, 30(7): 1625-1629. GE X, LIU F L, LU B, et al. Analysis for the cipherext characteristic of based on search mechanism chaotic cryptosystem[J]. Journal of Electronics & Information Technology, 2008, 30(7): 1625-1629. [16] 邓晓衡, 廖春龙, 朱从旭, 等. 像素位置与比特双重置乱的图像混沌加密算法[J]. 通信学报, 2014, 35(3): 216-223. DENG X H, LIAO C L, ZHU C X, et al. Image encryption algorithms based on chaos through dual scrambling of pixel position and bit[J]. Journal on Communications, 2014, 35(3): 216-223. [17] 张顺, 高铁杠. 基于类 DNA 编码分组与替换的加密方案[J]. 电子与信息学报, 2015, 37(1): 150-157. ZHANG S, GAO T G. Encryption based on DNA coding codon grouping and substitution[J]. Journal of Electronics & Information Technology, 2015, 37(1): 150-157. [18] 朱从旭, 胡玉平, 孙克辉. 基于超混沌系统和密文交错扩散的 图像加密新算法[J]. 电子与信息学报, 2012, 34(7): 1735-1743. ZHU C X, HU Y P, SUN K H. New image encryption algorithm based on hyperchaotic system and ciphertext diffusion in crisscross pattern[J]. Journal of Electronics & Information Technology, 2012, 34(7): 1735-1743. [19] 陈铁明, 葛亮. 面向无线传感器网络的混沌加密与消息鉴别算法[J]. 通信学报, 2013, 34(5): 113-120. CHEN T M, GE L. Chaos-based encryption and message authentication algorithm for wireless sensor network[J]. Journal on Communications, 2013, 34(5): 113-120. [20] 刘红军. 混沌理论在一次一密图像加密及保密通信系统中的应用研究[D]. 大连:大连理工大学,2014. LIU H J. Research on the application of chaos theory in one-time keys image encryption and secure communication system[D]. Dalian: Dalian University of Technology, 2014. [21] ABDULLAH H A, ABDULLAH H N, MAHMOUD AL-JAWHER W A. A hybrid chaotic map for communicationsecurity applications[J]. International Journal of Communication Systems, 2020, 33(4): e4236. [22] 樊春霞. 混沌保密通信系统的研究[D]. 南京: 南京航空航天大学, 2004. FAN C X. Research on chaotic secure communication system[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2004. [23] 陈云, 袁志民, 陈璐,等. 一类超混沌系统的全局有限时间同步与全局渐近同步[J]. 海军工程大学学报, 2022,34(1): 13-19. CHEN Y, YUAN Z M, CHEN L, et al. Global finite-time synchronization and globally asymptotical synchronization of a class of hyperchaotic systems[J]. 2022,34(1): 13-19. [24] 杨益飞, 骆敏舟, 张宏, 等. 永磁同步电动机系统与Rssler系统的自适应同步[J]. 制造技术与机床, 2020(1): 103-106. YANG Y F, LUO M Z, ZHANG H, et al. Adaptive control synchronization for PMSM and Rssler system[J]. Technology and Manufacture, 2020(1): 103-106. [25] 李善强, 彭秀艳, 李强. 多个时滞混沌系统自适应有限时间同步控制[J]. 电机与控制学报, 2019, 23(6): 3-9. LI S Q, PENG X Y, LI Q. Adaptive finite-time synchronization of multiple chaotic systems with time-varying delay[J]. Electric Machines and Control, 2019, 23(6): 3-9. [26] 李东, 邓良明, 杜永霞, 等. 分数阶超混沌Chen系统和分数阶超混沌Rssler系统的异结构同步[J]. 物理学报, 2012, 61(5): 51-59. LI D, DENG L M, DU Y X, et al. Synchronization for fractional order hyperchaotic Chen system and fractional order hyperchaotic Rssler system with different structure[J]. Acta Physica Sinica, 2012, 61(5): 51-59. [27] ZOU Y, DONNER R V, MARWAN N, et al. Complex network approaches to nonlinear time series analysis[J]. Physics Reports, 2019, 787:1-97.
