Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor |
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| Affiliation: | 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 |
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| 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. |
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| Keywords: | two-dimensional maps memristive maps hidden attractors bifurcation analysis extremely hidden multi-stability |
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