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.
作者
Li-Ping Zhang
Yang Liu
Zhou-ChaoWei
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,Zhenjiang 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)
基金
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)
the Excellent Scientific and Technological Innovation Team of Jiangsu University.
