A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit
1
School of Electronic and Information Engineering, Anshun University, Anshun 561000, China
2
School of Mechanical and Electrical Engineering, Tarim University, Alar 843300, China
3
School of Mathematics and Computer Science, Guizhou Education University, Guiyang 550018, China
*
Authors to whom correspondence should be addressed.
Entropy 2019, 21(10), 1026; https://doi.org/10.3390/e21101026
Received: 30 September 2019
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Revised: 17 October 2019
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Accepted: 20 October 2019
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Published: 22 October 2019
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors II)
As a new type of nonlinear electronic component, a memristor can be used in a chaotic system to increase the complexity of the system. In this paper, a flux-controlled memristor is applied to an existing chaotic system, and a novel five-dimensional chaotic system with high complexity and hidden attractors is proposed. Analyzing the nonlinear characteristics of the system, we can find that the system has new chaotic attractors and many novel quasi-periodic limit cycles; the unique attractor structure of the Poincaré map also reflects the complexity and novelty of the hidden attractor for the system; the system has a very high complexity when measured through spectral entropy. In addition, under different initial conditions, the system exhibits the coexistence of chaotic attractors with different topologies, quasi-periodic limit cycles, and chaotic attractors. At the same time, an interesting transient chaos phenomenon, one kind of novel quasi-periodic, and weak chaotic hidden attractors are found. Finally, we realize the memristor model circuit and the proposed chaotic system use off-the-shelf electronic components. The experimental results of the circuit are consistent with the numerical simulation, which shows that the system is physically achievable and provides a new option for the application of memristive chaotic systems.
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Keywords:
memristor model; memristive chaos; hidden attractor; spectral entropy; multi-type quasi-periodic
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MDPI and ACS Style
Liu, L.; Du, C.; Liang, L.; Zhang, X. A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit. Entropy 2019, 21, 1026. https://doi.org/10.3390/e21101026
AMA Style
Liu L, Du C, Liang L, Zhang X. A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit. Entropy. 2019; 21(10):1026. https://doi.org/10.3390/e21101026
Chicago/Turabian StyleLiu, Licai, Chuanhong Du, Lixiu Liang, and Xiefu Zhang. 2019. "A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit" Entropy 21, no. 10: 1026. https://doi.org/10.3390/e21101026
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