The Eigenvalue Complexity of Sequences in the Real Domain
Abstract
:1. Introduction
2. Eigenvalue for Real Number Sequences
2.1. Eigenvalue for Binary Sequences
- (1)
- The tuple xk−1xk…xN−1 does not belong to the vocabulary of a proper prefix of yN.
- (2)
- The tuple xkxk+1…xN−1 belongs to the vocabulary of a proper prefix of yN.
2.2. Eigenvalue of Sequences in the Real Domain
3. Two Examples
3.1. Eigenvalue of Uniformly Distributed Random Sequence
3.2. Eigenvalue of Logistic Chaotic Sequence
4. Measure the Complexity of Chaotic Sequences
- Chebyshev mapChebyshev map can be written as
- Sine mapSine map can be mathematically described as
- Tent mapTent map is a kind of piece-wise function, which can be described as
- Logistic mapThe Logistic map has already been described in Equation (17), which we omitted here to avoid redundancy.
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Liu, L.; Xiang, H.; Li, R.; Hu, H. The Eigenvalue Complexity of Sequences in the Real Domain. Entropy 2019, 21, 1194. https://doi.org/10.3390/e21121194
Liu L, Xiang H, Li R, Hu H. The Eigenvalue Complexity of Sequences in the Real Domain. Entropy. 2019; 21(12):1194. https://doi.org/10.3390/e21121194
Chicago/Turabian StyleLiu, Lingfeng, Hongyue Xiang, Renzhi Li, and Hanping Hu. 2019. "The Eigenvalue Complexity of Sequences in the Real Domain" Entropy 21, no. 12: 1194. https://doi.org/10.3390/e21121194