Design of a Network Permutation Entropy and Its Applications for Chaotic Time Series and EEG Signals

Figures

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  Figure 1. Bandt and Pompe patterns with d=3.

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  Figure 2. Building the network using the patterns and their weights.

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  Figure 3. Networks and the corresponding probability distributions of different signals. (a) The network of the random signal; (b) the probability distribution of the random signal; (c) the network of the periodic signal; (d) the probability distribution of the periodic signal; (e) the network of the simplified Lorenz system with c=2; (f) the probability distribution of the simplified Lorenz system with c=2; (g) the network of the logistic map with μ=4; (h) the probability distribution of the logistic map with μ=4.

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  Figure 4. Networks and the corresponding probability distributions of the logistic map with different d. (a) The network with d=4; (b) the probability distribution with d=4; (c) the network with d=5; (d) the probability distribution with d=5.

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  Figure 5. NPE measuring results versus the parameter error and different d.

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  Figure 6. Complexity analysis results of the logistic map with the parameter μ varying. (a) NPE; (b) PE.

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  Figure 7. Complexity analysis results of the simplified Lorenz system with the parameter c varying. (a) NPE; (b) PE.

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  Figure 8. LEs of the chaotic systems. (a) Logistic map with the parameter μ varying; (b) simplified Lorenz system with parameter c varying.

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  Figure 9. Complexity analysis results of the fractional-order Hénon map. (a) NPE; (b) PE.

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  Figure 10. NPE complexity analysis results of the fractional-order Hénon map in different parameter planes (a) Parameter plane b−υ; (b) parameter plane a−b with υ=1; (c) parameter plane a−b with υ=0.95; (d) parameter plane a−b with υ=0.9.

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  Figure 11. Complexity analysis results of the fractional-order simplified Lorenz system. (a) NPE; (b) PE.

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  Figure 12. Sample data of A050, C050, and E050.