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Article

A Fractional-Order Improved Quantum Logistic Map: Chaos, 0-1 Testing, Complexity, and Control

by
Birong Xu
1,*,
Ximei Ye
1,
Guangyi Wang
2,
Zhongxian Huang
3 and
Changwu Zhang
1
1
College of Mechanic and Electronic Engineering, Wuyi University, Wuyishan 354300, China
2
Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China
3
College of Mathematics and Computer Science, Wuyi University, Wuyishan 354300, China
*
Author to whom correspondence should be addressed.
Axioms 2023, 12(1), 94; https://doi.org/10.3390/axioms12010094
Submission received: 4 December 2022 / Revised: 7 January 2023 / Accepted: 10 January 2023 / Published: 16 January 2023
(This article belongs to the Topic Fractional Calculus: Theory and Applications)
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Abstract

Based on a quantum logistic map and a Caputo-like delta difference operator, a fractional-order improved quantum logistic map, which has hidden attractors, was constructed. Its dynamical behaviors are investigated by employing phase portraits, bifurcation diagrams, Lyapunov spectra, dynamical mapping, and 0-1 testing. It is shown that the proposed fractional-order map is influenced by both the parameters and the fractional order. Then, the complexity of the map is explored through spectral entropy and approximate entropy. The results show that the fractional-order improved quantum logistic map has stronger robustness within chaos and higher complexity, so it is more suitable for engineering applications. In addition, the fractional-order chaotic map can be controlled for different periodic orbits by the improved nonlinear mapping on the wavelet function.
Keywords: improved quantum logistic map; discrete fractional calculus; hidden attractor; chaos control improved quantum logistic map; discrete fractional calculus; hidden attractor; chaos control

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MDPI and ACS Style

Xu, B.; Ye, X.; Wang, G.; Huang, Z.; Zhang, C. A Fractional-Order Improved Quantum Logistic Map: Chaos, 0-1 Testing, Complexity, and Control. Axioms 2023, 12, 94. https://doi.org/10.3390/axioms12010094

AMA Style

Xu B, Ye X, Wang G, Huang Z, Zhang C. A Fractional-Order Improved Quantum Logistic Map: Chaos, 0-1 Testing, Complexity, and Control. Axioms. 2023; 12(1):94. https://doi.org/10.3390/axioms12010094

Chicago/Turabian Style

Xu, Birong, Ximei Ye, Guangyi Wang, Zhongxian Huang, and Changwu Zhang. 2023. "A Fractional-Order Improved Quantum Logistic Map: Chaos, 0-1 Testing, Complexity, and Control" Axioms 12, no. 1: 94. https://doi.org/10.3390/axioms12010094

APA Style

Xu, B., Ye, X., Wang, G., Huang, Z., & Zhang, C. (2023). A Fractional-Order Improved Quantum Logistic Map: Chaos, 0-1 Testing, Complexity, and Control. Axioms, 12(1), 94. https://doi.org/10.3390/axioms12010094

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