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

doi:10.1088/1674-1056/ac7294

中国物理B ›› 2022, Vol. 31 ›› Issue (10): 100503-100503.doi: 10.1088/1674-1056/ac7294

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

收稿日期:2022-03-13 修回日期:2022-05-10 出版日期:2022-10-16 发布日期:2022-09-30
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. 11972173 and 12172340).

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

Received:2022-03-13 Revised:2022-05-10 Online:2022-10-16 Published:2022-09-30
Contact: Hai-Bo Jiang E-mail:yctcjhb@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11972173 and 12172340).

摘要/Abstract

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 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.

关键词: two-dimensional maps, memristive maps, hidden attractors, bifurcation analysis, extremely hidden multi-stability

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.

Key words: two-dimensional maps, memristive maps, hidden attractors, bifurcation analysis, extremely hidden multi-stability

中图分类号: (Low-dimensional chaos)

05.45.Ac

05.45.Pq (Numerical simulations of chaotic systems)

Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超), Hai-Bo Jiang(姜海波), Wei-Peng Lyu(吕伟鹏), and Qin-Sheng Bi(毕勤胜). Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor[J]. 中国物理B, 2022, 31(10): 100503-100503.

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

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

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