Chin. Phys. B, 2022, Vol. 31(10): 100503    DOI: 10.1088/1674-1056/ac7294
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# Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

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,†, Wei-Peng Lyu(吕伟鹏)1,2, and 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. Engineering Department, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK;
4. School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
Abstract  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 multi-stability, 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.
Keywords:  two-dimensional maps      memristive maps      hidden attractors      bifurcation analysis      extremely hidden multi-stability
Received:  13 March 2022      Revised:  10 May 2022      Accepted manuscript online:
 PACS: 05.45.Ac (Low-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11972173 and 12172340).
Corresponding Authors:  Hai-Bo Jiang     E-mail:  yctcjhb@126.com