一种具有多对称同质吸引子的四维混沌系统的超级多稳定性研究  

Extreme Multi-stability of a Four-dimensional Chaotic System with Infinitely Many Symmetric Homogeneous Attractors

作　　者：黄丽莲[1,2] 姚文举 项建弘 王霖郁[1,2] HUANG Lilian;YAO Wenju;XIANG Jianhong;WANG Linyu(College of Information and Communication Engineering,Harbin Engineering University,Harbin 150001,China;The Key Laboratory of Advanced Ship Communication and Information Technology,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]哈尔滨工程大学信息与通信工程学院,哈尔滨150001 [2]哈尔滨工程大学先进船舶通信与信息技术重点实验室,哈尔滨150001

出　　处：《电子与信息学报》2022年第1期390-399,共10页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(61203004);黑龙江省自然科学基金(F201220);黑龙省自然科学基金联合引导项目(LH2020F022)。

摘　　要：该文在一个经典3维混沌系统的基础上提出一个新的具有超级多稳定性的4维混沌系统。新系统具有一个线平衡点,可以产生无限多对称的同质吸引子。通过相轨图和庞加莱截面等方法分析了系统的混沌特性。重点利用相轨图、分岔图和Lyapunov指数谱等方法分析了初始条件对系统超级多稳定性的影响,分析表明该系统具有很大的初值变化范围,除零点外恒定的Lyapunov指数谱,中心对称的离散分岔图。进一步地,该文研究了系统初值对称性与吸引子对称性的关系,不同于现有混沌系统中的对称吸引子,该系统可以产生无限多对称的同质吸引子。最后,利用电路仿真软件搭建模拟电路捕捉该系统的混沌吸引子,其结果验证了数值仿真的正确性。A new four-dimensional chaotic system with extreme multi-stability based on a classic threedimensional chaotic system is proposed.The new system has a line equilibrium point,which can generate an infinite number of symmetrical homogeneous attractors.The chaotic characteristics of the system are analyzed by phase orbit diagram and Poincarésection methods.Using phase orbit diagrams,bifurcation diagrams and Lyapunov exponent spectrum methods,the influence of initial conditions on the extreme multi-stability of the system is analyzed.The analysis shows that the system has a large initial value variation range,and the Lyapunov exponent spectrum is constant except for the zero point.In addition,the system also has centrally symmetrical discrete bifurcation diagrams.Furthermore,the relationship between the initial symmetry of the system and the symmetry of the attractor is studied,which is different from the symmetrical attractor in the existing chaotic system,which can generate an infinite number of symmetrical homogeneous attractors.Finally,circuit simulation software is used to build an analog circuit to capture the chaotic attractor of the system,and the result verifies the correctness of the numerical simulation.

关 键 词：超级多稳定性 无限多对称的同质吸引子 中心对称的离散分岔图 

分 类 号：TP271[自动化与计算机技术—检测技术与自动化装置]