类元素周期律框架下新混沌系统的构造方法研究  

Study on the New Chaotic Attractor Based on Periodic Law Frame

作　　者：王伟豪 刘树勇[1] 柴凯 杨庆超[2] 王梦同 WANG Wei-hao;LIU Shu-yong;CHAI Kai;YANG Qing-chao;WANG Meng-tong(College of Power Engineering,Naval University of Engineering,Wuhan 430033,China;College of Naval Architecture and Ocean,Naval University of Engineering,Wuhan 430033,China)

机构地区：[1]海军工程大学动力工程学院,武汉430033 [2]海军工程大学舰船与海洋学院,武汉430033

出　　处：《武汉理工大学学报》2020年第5期77-85,共9页Journal of Wuhan University of Technology

基　　金：国家自然科学基金(51579242,51509253,51679245);湖北省自然科学基金(2020CFB148)。

摘　　要：针对混沌系统构造复杂缺乏系统理论依据的问题,提出了构建新混沌系统的类元素周期律框架,在此基础上构造了新混沌系统,分析了系统的基本组成并与经典混沌系统进行了比较,该系数矩阵满足混沌系统系数准则。探讨了该系统的局部动力学特征,计算了不同参数条件下的Lyapunov指数谱,给出了响应随参数变化的全局分岔图,分析了响应的Poincaré截面图,并得到了与系统Lyapunov指数参数对应的基本运动模式分布图。A kind of periodic table-like frame used to construct new chaotic system is presented,and a novel chaotic attractor is constructed.The basic structure of the system is analyzed and compared with the classic chaotic system.The coefficient matrix is satisfied with the chaos family coefficient criteria.The local dynamic characteristic is studied and the Lyapunov exponent spectrum is calculated under different parameters.The global bifurcation diagram is illustrated,and Poincarésection diagram is obtained.Finally,the basic motion mode is discussed with the Lyapunov exponent parameter surface.

关 键 词：新混沌系统 吸引子 LYAPUNOV指数谱 分岔图 

分 类 号：TB535[理学—物理] O322[理学—声学]