{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:03:34Z","timestamp":1772294614229,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,2]]},"abstract":"<jats:p>In this paper, we consider a linear wave equation on an interval with a van der Pol nonlinear boundary condition at one end and an energy-pumping condition at the other end. We study the dynamical behavior of the Riemann invariants (u,v) of the wave equation in terms of the growth rates of the total variations of the snapshots on the spatial interval. Our main contributions here are the detection of rapid fluctuations of the snapshots of u and v in the long run. The results here sharpen those in the earlier works of [Chen et al., 2001] and [Huang, 2003].<\/jats:p>","DOI":"10.1142\/s0218127405012223","type":"journal-article","created":{"date-parts":[[2005,5,10]],"date-time":"2005-05-10T11:32:19Z","timestamp":1115724739000},"page":"567-580","source":"Crossref","is-referenced-by-count":27,"title":["RAPID FLUCTUATIONS OF SNAPSHOTS OF ONE-DIMENSIONAL LINEAR WAVE EQUATION WITH A VAN DER POL NONLINEAR BOUNDARY CONDITION"],"prefix":"10.1142","volume":"15","author":[{"given":"YU","family":"HUANG","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JUN","family":"LUO","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ZUOLING","family":"ZHOU","sequence":"additional","affiliation":[{"name":"Lingnan School, Zhongshan University, Guangzhou 510275, 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":"10.1090\/S0002-9939-1978-0509258-X"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084762"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-98-02022-4"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498000280"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498000292"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1063\/1.532670"},{"key":"rf7","doi-asserted-by":"crossref","unstructured":"G.\u00a0Chen, Control of Nonlinear Distributed Parameter System, Lecture Notes in Pure and Applied Mathematics Series\u00a0218, eds. G.\u00a0Chen, I.\u00a0Lascieka and J.\u00a0Zhou (Marcel Dekker, NY, 2001)\u00a0pp. 15\u201342.","DOI":"10.1201\/9780203904190"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004504"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404010540"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403007138"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-6262-3"},{"key":"rf13","volume-title":"Symbolic Dynamics (in Chinese)","author":"Zhou Z. L.","year":"1997"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405012223","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,10]],"date-time":"2021-07-10T20:43:26Z","timestamp":1625949806000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405012223"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,2]]},"references-count":12,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,2]]}},"alternative-id":["10.1142\/S0218127405012223"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405012223","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,2]]}}}