Dynamical Analysis of a Class of Memristor Chaotic Systems
ZHOU Wenjing, ZHANG Fuchen, CHEN Xiusu, CHEN Song
a. School of Mathematics and Statistics; b. Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, Chongqing Technology and Business University, Chongqing 400067, China
Abstract：To find new chaotic systems in electronics and circuits, a new class of four-dimensional chaotic systems based on memristor elements are proposed in this paper. We study the nonlinear dynamical behaviors of this kind of chaotic system, and finds that this kind of system has dissipative property. At the same time, we reveal the bifurcation and chaos phenomenon of this four-dimensional chaotic system from the aspects of chaotic attractors, Poincare section, the Lyapunov exponent, initial value sensitivity and bifurcation diagram by using theoretical and numerical analysis methods. Moreover, we find that the system is sensitive to the parameters and the initial values. And the system has the characteristics of multistability of chaotic flows.
[1] CHUA L O. Memristor-the missing circuit element[J]. IEEE Transactions on Circuit Theory, 1971, 18(5): 507-519. [2] STRUKOV D B, SNIDER G S, STEWART D R, et al. The missing memristor found[J]. Nature, 2008, 453(7191): 80-83. [3] 秦铭宏,赖强,吴永红.具有无穷共存吸引子的简单忆阻混沌系统的分析与实现[J].物理学报,2022,71(16):146-156. QIN M H, LAI Q, WU Y H. Analysis and implementation of simple memristive chaotic system with infinite coexisting attractors[J]. Acta Physica Sinica, 2022, 71(16): 146-156. [4] 张国桢, 王聪, 张宏立. 一种含隐藏吸引子的新型忆阻超混沌系统[J].固体电子学研究与进展,2023,43(4):335-340. ZHANG G Z, WANG C, ZHANG H L. A new memristive hyperchaotic system with hidden attractors[J]. Research and Progress in Solid Electronics, 2023, 43(4): 335-340. [5] 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 memristive hyperchaotic system[J]. Complex Systems and Complexity Science, 2023, 20(2): 43-51. [6] 万求真,马婧,计文奎,等.无平衡点忆阻超混沌系统的动力学分析及电路实现[J].固体电子学研究与进展, 2023, 43(3):227-233,271. WAN Q Z, MA J, JI W K, et al. Dynamic analysis and circuit implementation of memristive hyperchaotic system without equilibrium point[J]. Research and Progress in Solid Electronics, 2023, 43(3): 227-233,271. [7] 夏国莹,曾以成.一类忆阻型4D保守混沌系统的设计及其分析[J].电子元件与材料,2023,42(6):704-713. XIA G Y, ZENG Y C. Design and analysis of a type of memristive 4D conservative chaotic system[J]. Electronic Components and Materials, 2023, 42(6): 704-713. [8] 毛北行, 王东晓. 分数阶永磁同步电机混沌系统自适应滑模同步[J]. 浙江大学学报(理学版), 2023, 50(5): 564-568. MAO B X, WANG D X. Adaptive sliding mode synchronization of fractional-order permanent magnet synchronous motor chaotic system[J]. Journal of Zhejiang University (Science Edition), 2023, 50(5): 564-568. [9] 颜闽秀, 张萍. 具有隐藏吸引子的新四维混沌系统的共存现象及图像加密[J]. 山东科技大学学报(自然科学版), 2023, 42(4): 113-126. YAN M X, ZHANG P. Coexistence phenomenon and image encryption of new four-dimensional chaotic systems with hidden attractors[J]. Journal of Shandong University of Science and Technology (Natural Science Edition), 2023, 42(4): 113-126. [10] 何纪辉,王倩,赵瑛.基于双混沌系统与DNA动态编码的医学图像加密算法[J].国外电子测量技术,2023,42(8): 124-131. HE J H, WANG Q, ZHAO Y. Medical image encryption algorithm based on dual chaotic system and DNA dynamic coding[J]. Foreign Electronic Measurement Technology, 2023, 42(8): 124-131. [11] 钟鸣,刘建东,刘博,等. 基于Spark与混沌系统的图像加密算法[J].计算机应用与软件,2023,40(8):342-349. ZHONG M, LIU J D, LIU B, et al. Image encryption algorithm based on Spark and chaos system[J]. Computer Applications and Software, 2023, 40(8): 342-349. [12] 孟晓玲, 毛北行. 分数阶和整数阶含对数项T混沌系统自适应滑模同步[J]. 吉林大学学报(理学版), 2023, 61(4): 937-942. MENG X L, MAO B X. Adaptive sliding mode synchronization of fractional-order and integer-order T-chaotic systems containing logarithmic terms[J]. Journal of Jilin University (Science Edition), 2023, 61(4): 937-942. [13] 覃祖和, 秦为民. 新型混沌电路系统构建及其在故障检测方向的应用[J]. 中国农机化学报, 2023, 44(5): 155-160. QIN Z H, QIN W M. Construction of a new chaotic circuit system and its application in fault detection[J]. Chinese Journal of Agricultural Mechanization, 2023, 44(5): 155-160. [14] 王茜, 刘恒. 不同维分数阶混沌系统的自适应模糊滑模有限时间同步控制[J]. 模糊系统与数学, 2023, 37(2): 1-12. WANG Q, LIU H. Adaptive fuzzy sliding mode finite-time synchronization control of fractional-order chaotic systems with different dimensions[J]. Fuzzy Systems and Mathematics, 2023, 37(2): 1-12. [15] 赖强, 刘子怡. 含多吸引和调幅特性的新混沌系统分析与实现[J]. 大连工业大学学报, 2023, 42(2): 143-150. LAI Q, LIU Z Y. Analysis and implementation of new chaotic systems with multiple attraction and amplitude modulation characteristics[J]. Journal of Dalian University of Technology, 2023, 42(2): 143-150. [16] 王春娥,崔岩,王申鹏,等. 整数阶及分数阶超混沌系统的有限时间同步控制[J].江苏科技大学学报(自然科学版), 2023, 37(1):109-113. WANG C E, CUI Y, WANG S P, et al. Finite time synchronization control of integer-order and fractional-order hyperchaotic systems[J]. Journal of Jiangsu University of Science and Technology (Natural Science Edition), 2023, 37(1): 109-113. [17] 颜闽秀, 谢俊红, 张帅. 具有多稳态和可调数目吸引子共存的混沌系统[J]. 兰州理工大学学报, 2022, 48(6): 88-95. YAN M X, XIE J H, ZHANG S. Chaotic system with coexistence of multistable states and adjustable number of attractors[J]. Journal of Lanzhou University of Science and Technology, 2022, 48(6): 88-95. [18] 徐昌彪,吴霞,马珺杰,等.具有多种平衡点类型的新型三维混沌系统[J].重庆邮电大学学报(自然科学版),2021, 33(2):319-329. XU C B, WU X, MA J J, et al. New three-dimensional chaotic system with multiple equilibrium point types[J]. Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition), 2021, 33(2): 319- 329. [19] 颜闽秀, 徐辉. 四翼混沌系统分析和同步控制[J]. 控制工程, 2021, 28(4): 681-686. YAN M X, XU H. Analysis and synchronous control of four-wing chaotic system[J]. Control Engineering, 2021, 28(4): 681-686. [20] MUTHUSWAMY B, CHUA L O. Simplest chaotic circuit[J]. International Journal of Bifurcation and Chaos, 2010, 20(5): 1567 -1580. [21] 陈关荣, 吕金虎. Lorenz系统族的动力学分析、控制与同步[M]. 北京: 科学出版社, 2003.
