A Novel Four-Dimensional Memristive Hyperchaotic Map Based on a Three-Dimensional Parabolic Chaotic Map with a Discrete Memristor

Recently, the application of memristors in chaotic systems has been extensively studied. Unfortunately, there is limited literature on the introduction of discrete memristors into chaotic maps, especially into non-classical multidimensional maps. For this reason, this paper establishes a new three-d...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 15; no. 10; p. 1879
Main Authors Wang, Mengjiao, Tong, Luyao, Li, Chunlai, Zhang, Xinan, Iu, Herbert Ho-Ching, Li, Zhijun
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2023
Subjects
attractor coexistence
bifurcation
Chaos theory
chaotic map
coupled chaos
discrete memristor
Dynamic stability
Eigenvalues
hyperchaos
Iterative methods
Memristors
Phase diagrams
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Summary:Recently, the application of memristors in chaotic systems has been extensively studied. Unfortunately, there is limited literature on the introduction of discrete memristors into chaotic maps, especially into non-classical multidimensional maps. For this reason, this paper establishes a new three-dimensional parabolic chaotic map model; in order to improve the complexity and randomness of the map, it is coupled with a square-charge-controlled discrete memristor to design a new four-dimensional memristive hyperchaotic map. Firstly, the stability of the two maps is discussed. And their dynamical properties are compared using Lyapunov exponential spectra and bifurcation diagrams. Then, the phase diagram and iteration sequence of the 4D memristive hyperchaotic map are obtained. Meanwhile, we investigate the hyperchaotic states, the transient chaos, state transfer and attractor coexistence phenomena of the four-dimensional memristive map. In particular, the special state transfer phenomenon of switching from a periodic attractor to a quasi-periodic attractor and the special coexistence phenomenon of a quasi-periodic attractor coexisting with a quasi-periodic attractor around fixed points are found, which have not been observed in other systems. Finally, the phase-track diagrams and iterative sequence diagrams of the four-dimensional memristive map are verified on a digital experimental platform, revealing its potential for practical applications.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15101879