A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors

doi:10.1088/1674-1056/ab8626

中国物理B ›› 2020, Vol. 29 ›› Issue (6): 60501-060501.doi: 10.1088/1674-1056/ab8626

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors

Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超), Hai-Bo Jiang(姜海波), Qin-Sheng Bi(毕勤胜)

1 Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 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 EX4 4QF, UK;
4 School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

收稿日期:2020-02-08 修回日期:2020-03-16 出版日期:2020-06-05 发布日期:2020-06-05
通讯作者: Hai-Bo Jiang E-mail:yctcjhb@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11672257, 11632008, 11772306, and 11972173), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20161314), the 5th 333 High-level Personnel Training Project of Jiangsu Province of China (Grant No. BRA2018324), and the Excellent Scientific and Technological Innovation Team of Jiangsu University.

A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors

Li-Ping Zhang(张丽萍)^1,2, Yang Liu(刘洋)³, Zhou-Chao Wei(魏周超)⁴, Hai-Bo Jiang(姜海波)², Qin-Sheng Bi(毕勤胜)¹

1 Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 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 EX4 4QF, UK;
4 School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

Received:2020-02-08 Revised:2020-03-16 Online:2020-06-05 Published:2020-06-05
Contact: Hai-Bo Jiang E-mail:yctcjhb@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11672257, 11632008, 11772306, and 11972173), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20161314), the 5th 333 High-level Personnel Training Project of Jiangsu Province of China (Grant No. BRA2018324), and the Excellent Scientific and Technological Innovation Team of Jiangsu University.

摘要/Abstract

摘要： We study a novel class of two-dimensional maps with infinitely many coexisting attractors. Firstly, the mathematical model of these maps is formulated by introducing a sinusoidal function. The existence and the stability of the fixed points in the model are studied indicating that they are infinitely many and all unstable. In particular, a computer searching program is employed to explore the chaotic attractors in these maps, and a simple map is exemplified to show their complex dynamics. Interestingly, this map contains infinitely many coexisting attractors which has been rarely reported in the literature. Further studies on these coexisting attractors are carried out by investigating their time histories, phase trajectories, basins of attraction, Lyapunov exponents spectrum, and Lyapunov (Kaplan-Yorke) dimension. Bifurcation analysis reveals that the map has periodic and chaotic solutions, and more importantly, exhibits extreme multi-stability.

关键词: two-dimensional map, infinitely many coexisting attractors, extreme multi-stability, chaotic attractor

Abstract: We study a novel class of two-dimensional maps with infinitely many coexisting attractors. Firstly, the mathematical model of these maps is formulated by introducing a sinusoidal function. The existence and the stability of the fixed points in the model are studied indicating that they are infinitely many and all unstable. In particular, a computer searching program is employed to explore the chaotic attractors in these maps, and a simple map is exemplified to show their complex dynamics. Interestingly, this map contains infinitely many coexisting attractors which has been rarely reported in the literature. Further studies on these coexisting attractors are carried out by investigating their time histories, phase trajectories, basins of attraction, Lyapunov exponents spectrum, and Lyapunov (Kaplan-Yorke) dimension. Bifurcation analysis reveals that the map has periodic and chaotic solutions, and more importantly, exhibits extreme multi-stability.

Key words: two-dimensional map, infinitely many coexisting attractors, extreme multi-stability, chaotic attractor

中图分类号: (Low-dimensional chaos)

05.45.Ac

05.45.Pq (Numerical simulations of chaotic systems)

张丽萍, 刘洋, 魏周超, 姜海波, 毕勤胜. A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors[J]. 中国物理B, 2020, 29(6): 60501-060501.

Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超), Hai-Bo Jiang(姜海波), Qin-Sheng Bi(毕勤胜). A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors[J]. Chin. Phys. B, 2020, 29(6): 60501-060501.

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A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors

A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors

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