{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:13:55Z","timestamp":1773656035413,"version":"3.50.1"},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2002,6]]},"abstract":"<jats:p>In this Letter, we study the popular parametric variation chaos control and state-feedback methodologies in chaos control, and point out for the first time that they are actually equivalent in the sense that there exist diffeomorphisms that can convert one to the other for most smooth chaotic systems. Detailed conversions are worked out for typical discrete chaotic maps (logistic, H\u00e9non) and continuous flows (R\u00f6sller, Lorenz) for illustration. This unifies the two seemingly different approaches from the physics and the engineering communities on chaos control. This new perspective reveals some new potential applications such as chaos synchronization and normal form analysis from a unified mathematical point of view.<\/jats:p>","DOI":"10.1142\/s0218127402005194","type":"journal-article","created":{"date-parts":[[2002,7,28]],"date-time":"2002-07-28T23:09:56Z","timestamp":1027897796000},"page":"1411-1415","source":"Crossref","is-referenced-by-count":6,"title":["ON THE RELATIONSHIP BETWEEN PARAMETRIC VARIATION AND STATE FEEDBACK IN CHAOS CONTROL"],"prefix":"10.1142","volume":"12","author":[{"given":"ZENGRONG","family":"LIU","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GUANRONG","family":"CHEN","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, City University of Hong Kong, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/3033"},{"key":"rf2","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1142\/S0218127400000360","volume":"10","author":"Chen G.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.1196"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4740-9"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4067-7"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127402005194","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,6]],"date-time":"2020-03-06T05:31:30Z","timestamp":1583472690000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127402005194"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":5,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2002,6]]}},"alternative-id":["10.1142\/S0218127402005194"],"URL":"https:\/\/doi.org\/10.1142\/s0218127402005194","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}