{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:52:08Z","timestamp":1760784728728,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,30]],"date-time":"2019-08-30T00:00:00Z","timestamp":1567123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the China Postdoctoral Science Foundation grant number","award":["2019M652791"],"award-info":[{"award-number":["2019M652791"]}]},{"name":"the Postdoctoral Innovative Talents Support Program grant number","award":["BX20180386"],"award-info":[{"award-number":["BX20180386"]}]},{"name":"the Natural Science Foundation of Hunan Province","award":["2019JJ5041, S2019JJSSLH0130"],"award-info":[{"award-number":["2019JJ5041, S2019JJSSLH0130"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11847159, 11747150, 61161006 and 61573383"],"award-info":[{"award-number":["11847159, 11747150, 61161006 and 61573383"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Measuring the complexity of time series provides an important indicator for characteristic analysis of nonlinear systems. The permutation entropy (PE) is widely used, but it still needs to be modified. In this paper, the PE algorithm is improved by introducing the concept of the network, and the network PE (NPE) is proposed. The connections are established based on both the patterns and weights of the reconstructed vectors. The complexity of different chaotic systems is analyzed. As with the PE algorithm, the NPE algorithm-based analysis results are also reliable for chaotic systems. Finally, the NPE is applied to estimate the complexity of EEG signals of normal healthy persons and epileptic patients. It is shown that the normal healthy persons have the largest NPE values, while the EEG signals of epileptic patients are lower during both seizure-free intervals and seizure activity. Hence, NPE could be used as an alternative to PE for the nonlinear characteristics of chaotic systems and EEG signal-based physiological and biomedical analysis.<\/jats:p>","DOI":"10.3390\/e21090849","type":"journal-article","created":{"date-parts":[[2019,8,30]],"date-time":"2019-08-30T10:31:17Z","timestamp":1567161077000},"page":"849","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Design of a Network Permutation Entropy and Its Applications for Chaotic Time Series and EEG Signals"],"prefix":"10.3390","volume":"21","author":[{"given":"Bo","family":"Yan","sequence":"first","affiliation":[{"name":"College of Computer and Electrical Engineering, Hunan University of Arts and Science, Changde 415000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5190-4841","authenticated-orcid":false,"given":"Shaobo","family":"He","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kehui","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2027","DOI":"10.1016\/j.eswa.2007.12.065","article-title":"Automatic detection of epileptic seizures in EEG using discrete wavelet transform and approximate entropy","volume":"36","author":"Ocak","year":"2009","journal-title":"Expert Syst. 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