SCIENTIA SINICA Informationis, Volume 49 , Issue 9 : 1205-1216(2019) https://doi.org/10.1360/N112018-00197

Generalized phase permutation entropy algorithm based on two-index entropy

• AcceptedDec 13, 2018
• PublishedAug 30, 2019
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References

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• Figure 1

(Color online) Comparison of two kinds of entropy for the logistic map dynamic changes detection when $m=3$, $\tau=1$. (a) Generalized permutation entropy $({\rm~PE}_{q,\delta})$; (b) generalized phase permutation entropy $({\rm~PPE}_{q,\delta})$

• Figure 2

(Color online) Detecting dynamic changes in logistic map using ${\rm~PE}_{q,\delta}$ and ${\rm~PPE}_{q,\delta}$ when $m=5$, $\tau=1$, $0<q\leq2$, $\delta=1$. (a) ${\rm~PE}_{q,1}$ when $0<q\leq2$; (b) ${\rm~PPE}_{q,1}$ when $0<q\leq2$

• Figure 3

(Color online) Detecting dynamic changes in logistic map using ${\rm~PE}_{q,\delta}$ and ${\rm~PPE}_{q,\delta}$ when $m=5$, $\tau=1$, $-2<q\leq0$, $\delta=1$. (a) The ${\rm~PE}_{q,1}$ when $-2<q\leq0$; (b) the ${\rm~PPE}_{q,1}$ when $-2<q\leq0$

• Figure 4

(Color online) Detecting dynamic changes in logistic map using ${\rm~PE}_{q,\delta}$ and ${\rm~PPE}_{q,\delta}$ when $m=5$, $\tau=1$, $q=1$, $0<\delta\leq2$. (a) The ${\rm~PE}_{1,\delta}$ when $0<\delta\leq2$; (b) the ${\rm~PPE}_{1,\delta}$ when $0<\delta\leq2$

• Figure 5

(Color online) Detecting dynamic changes in logistic map using ${\rm~PE}_{q,\delta}$ and ${\rm~PPE}_{q,\delta}$ when $m=5$, $\tau=1$, $q=1$, $-2<\delta\leq0$. (a) The ${\rm~PE}_{1,\delta}$ when $-2<\delta\leq0$; (b) the ${\rm~PPE}_{1,\delta}$ when $-2<\delta\leq0$

• Figure 6

(Color online) Detecting dynamic changes in logistic map with different value of $q$, $\delta$ using ${\rm~PE}_{q,\delta}$ and ${\rm~PPE}_{q,\delta}$ when $m=5$, $\tau=1$. (a) The generalized permutation entropy $({\rm~PE}_{q,\delta})$; (b) the generalized phase permutation entropy $({\rm~PPE}_{q,\delta})$

• Figure 7

(Color online) The ${\rm~PE}_{q,\delta}$ and ${\rm~PPE}_{q,\delta}$ in different length of data and signal-to-noise ration (SNR) when $m=5$, $\tau=1$. (a) The sequence of Gaussian wave packets; (a1) enlarged view of each wave packet in a Gaussian wave packet sequence; (b) the ${\rm~PE}_{q,\delta}$ and ${\rm~PPE}_{q,\delta}$ in different length of data when $m=5$, $\tau=1$; (c) the ${\rm~PE}_{q,\delta}$ and ${\rm~PPE}_{q,\delta}$ in different SNR when $m=5$, $\tau=1$

• Figure 8

(Color online) ${\rm~PE}_{q,\delta}$ vs. ${\rm~PPE}_{q,\delta}$ in the case of the VT signal when $m=5$, $\tau=1$. (a) The VT signal;protect łinebreak (b) comparison between ${\rm~PE}_{q,\delta}$ with different parameters $q$, $\delta$ for the VT signal; (c) comparison between ${\rm~PPE}_{q,\delta}$ with different parameters $q$, $\delta$ for the VT signal

• Figure 9

(Color online) ${\rm~PE}_{q,\delta}$ vs. ${\rm~PPE}_{q,\delta}$ in the case of the VFL signal when $m=5$, $\tau=1$. (a) The VFL signal;protect łinebreak (b) comparison between ${\rm~PE}_{q,\delta}$ with different parameters $q$, $\delta$ for the VFL signal; (c) comparison between ${\rm~PPE}_{q,\delta}$ with different parameters $q$, $\delta$ for the VFL signal

• Figure 10

(Color online) ${\rm~PE}_{q,\delta}$ vs. ${\rm~PPE}_{q,\delta}$ in the case of the VF signal when $m=5$, $\tau=1$. (a) The VF signal;protect łinebreak (b) comparison between ${\rm~PE}_{q,\delta}$ with different parameters $q$, $\delta$ for the VF signal; (c) comparison between ${\rm~PPE}_{q,\delta}$ with different parameters $q$, $\delta$ for the VF signal

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