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

doi:10.1088/1674-1056/ac7294

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

Cite this article:

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 2022 Chin. Phys. B 31 100503

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

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