A class of two-dimensional rational maps with self-excited and hidden attractors  

作　　者：Li-Ping Zhang Yang Liu Zhou-Chao Wei Hai-Bo Jiang Qin-Sheng Bi 张丽萍;刘洋;魏周超;姜海波;毕勤胜(Faculty of Civil Engineering and Mechanics,Jiangsu University,Zhenjang 212013,China;School of Mathematics and Statistics,Yancheng Teachers University,Yancheng 224002,China;College of Engineering,Mathematics and Physical Sciences,University of Exeter,Exeter EX44QF,UK;School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]Faculty of Civil Engineering and Mechanics,Jiangsu University,Zhenjang 212013,China [2]School of Mathematics and Statistics,Yancheng Teachers University,Yancheng 224002,China [3]College of Engineering,Mathematics and Physical Sciences,University of Exeter,Exeter EX44QF,UK [4]School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China

出　　处：《Chinese Physics B》2022年第3期224-233,共10页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant Nos. 11672257, 11772306, 11972173, and 12172340);the 5th 333 High-level Personnel Training Project of Jiangsu Province of China (Grant No. BRA2018324)。

摘　　要：This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov(Kaplan–Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work.

关 键 词：two-dimensional rational map hidden attractors multi-stability a line of fixed points chaotic attractor 

分 类 号：O177.91[理学—数学] O415.5[理学—基础数学]