{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:54:03Z","timestamp":1772286843077,"version":"3.50.1"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,11]]},"abstract":"<jats:p> We consider a system of autonomous ODE's which is S<jats:sup>1<\/jats:sup>-equivariant and has a family of asymptotically stable modulated wave solutions with wave frequency \u03b1<jats:sub>0<\/jats:sub> and modulation frequency \u03b2<jats:sub>0<\/jats:sub>. This system will be perturbed, where the applied nonautonomous force also represents a modulated wave, but with wave frequency \u03b1 and modulations frequency \u03b2. The strength of this perturbation is not necessarily small. Our goal is to look for conditions such that the perturbed system exhibits an approximate entrainment of the modulation frequency \u03b2 on any given finite time interval, where the approximation error can be controlled by the wave frequency. <\/jats:p>","DOI":"10.1142\/s0218127405014234","type":"journal-article","created":{"date-parts":[[2006,2,6]],"date-time":"2006-02-06T04:49:18Z","timestamp":1139201358000},"page":"3579-3588","source":"Crossref","is-referenced-by-count":2,"title":["ENTRAINMENT OF MODULATION FREQUENCY: A CASE STUDY"],"prefix":"10.1142","volume":"15","author":[{"given":"KLAUS R.","family":"SCHNEIDER","sequence":"first","affiliation":[{"name":"Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstra\u00dfe 39, 10117 Berlin, Germany"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"1981","volume":"219","author":"Afraimovich V. S.","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"rf2","first-page":"734","volume":"5","author":"Afraimovich V. S.","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/68.248419"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4211-4"},{"key":"rf5","unstructured":"M.\u00a0Radziunas and H.J.\u00a0W\u00fcnsche, Optoelectronic Devices, ed. J.\u00a0Piprek (Springer, 2004)\u00a0pp. 121\u2013150."},{"key":"rf6","first-page":"1","volume":"75","author":"Rand D.","journal-title":"Arch. Rat. Mech. Anal."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1997.3379"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405014234","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T11:03:26Z","timestamp":1565175806000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405014234"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,11]]},"references-count":7,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,11]]}},"alternative-id":["10.1142\/S0218127405014234"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405014234","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,11]]}}}