A class of two-dimensional rational maps with self-excited and hidden attractors. (1st February 2022)

• Record Type: Journal Article
• Authors: Zhang 张, Li-Ping 丽萍; Liu 刘, Yang 洋; Wei 魏, Zhou-Chao 周超; Jiang 姜, Hai-Bo 海波; Bi 毕, Qin-Sheng 勤胜
• Is Part Of: Chinese physics B. Volume 31:Number 3(2022)
• Publication Date: 2022-02-01
• Subjects: two-dimensional rational map -- hidden attractors -- multi-stability -- a line of fixed points -- chaotic attractor; 05.45.Ac -- 05.45.Pq; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1674-1056/ac4025
• Languages: English
• ISSNs: 1674-1056

Abstract

Abstract : 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.