Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor  

作　　者：Li-Ping Zhang Yang Liu Zhou-Chao Wei Hai-Bo Jiang Wei-Peng Lyu Qin-Sheng Bi 张丽萍;刘洋;魏周超;姜海波;吕伟鹏;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;Engineering Department,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,Zhenjiang 212013,China [2]School of Mathematics and Statistics,Yancheng Teachers University,Yancheng 224002,China [3]Engineering Department,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10期331-340,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. 11972173 and 12172340)。

摘　　要：We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction,bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multistability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially,this work can be used for some real applications in secure communication, such as data and image encryptions.

关 键 词：two-dimensional maps memristive maps hidden attractors bifurcation analysis extremely hidden multi-stability 

分 类 号：TN60[电子电信—电路与系统]