{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T09:36:26Z","timestamp":1775122586161,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2008,9]]},"abstract":"<jats:p> The mixing property is characterized by the metric entropy that is introduced by Kolmogorov for dynamical systems. The Kolmogorov entropy is infinite for a stochastic system. In this work, a relative metric entropy is considered. The relative metric entropy allows to estimate the level of mixing in noisy dynamical systems. An algorithm for calculating the relative metric entropy is described and examples of the metric entropy estimation are provided for certain chaotic systems with various noise intensities. The results are compared to the entropy estimation given by the positive Lyapunov exponents. <\/jats:p>","DOI":"10.1142\/s021812740802210x","type":"journal-article","created":{"date-parts":[[2008,11,28]],"date-time":"2008-11-28T11:12:56Z","timestamp":1227870776000},"page":"2851-2855","source":"Crossref","is-referenced-by-count":11,"title":["RELATIVE KOLMOGOROV ENTROPY OF A CHAOTIC SYSTEM IN THE PRESENCE OF NOISE"],"prefix":"10.1142","volume":"18","author":[{"given":"VADIM S.","family":"ANISHCHENKO","sequence":"first","affiliation":[{"name":"Saratov State University, 83, Astrakhanskaya Street, Saratov 410026, Russia"}]},{"given":"SERGEY","family":"ASTAKHOV","sequence":"additional","affiliation":[{"name":"Saratov State University, 83, Astrakhanskaya Street, Saratov 410026, Russia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Complicated Oscillations in Simple Systems","author":"Anishchenko V. S.","year":"1990"},{"key":"rf2","first-page":"163","volume":"48","author":"Anishchenko V. S.","journal-title":"Physics\u2013Uspekhi"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12878-7"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(98)00177-8"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.50.346"},{"key":"rf6","first-page":"754","volume":"124","author":"Kolmogorov A. N.","journal-title":"Docl. Russ. Acad. Sci."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2006.11.001"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1070\/RM1977v032n04ABEH001639"},{"key":"rf9","first-page":"397","volume":"35","author":"R\u00f6ssler O. E.","journal-title":"Phys. Lett. A"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812740802210X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:00:06Z","timestamp":1565190006000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812740802210X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9]]},"references-count":10,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,9]]}},"alternative-id":["10.1142\/S021812740802210X"],"URL":"https:\/\/doi.org\/10.1142\/s021812740802210x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9]]}}}