{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:51:42Z","timestamp":1772290302770,"version":"3.50.1"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2000,7]]},"abstract":"<jats:p> We consider discretized systems of hyperbolic balance laws. Decoupling of the flow, associated with a central difference scheme, can lead to binary oscillations \u2014 even and odd numbered grid points, separately, provide time-evolutions of two distinct, different, separate profiles. <\/jats:p><jats:p> Investigating the stability of this decoupling phenomenon, we encounter Hopf-like bifurcations in the absence of parameters. With some computer-algebra assistance, we describe the qualitative behavior near these bifurcation points. In particular we observe distinct even\/odd profiles which oscillate periodically in time and, for arbitrarily fine discretization, exhibit preferred, nonzero phase relationships between adjacent discretization points. <\/jats:p>","DOI":"10.1142\/s0218127400001018","type":"journal-article","created":{"date-parts":[[2003,5,7]],"date-time":"2003-05-07T04:18:55Z","timestamp":1052281135000},"page":"1613-1621","source":"Crossref","is-referenced-by-count":26,"title":["GENERIC HOPF BIFURCATION FROM LINES OF EQUILIBRIA WITHOUT PARAMETERS III: BINARY OSCILLATIONS"],"prefix":"10.1142","volume":"10","author":[{"given":"BERNOLD","family":"FIEDLER","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik I, Freie  Universit\u00e4t Berlin, Arnimallee 2-6, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"STEFAN","family":"LIEBSCHER","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik I, Freie  Universit\u00e4t Berlin, Arnimallee 2-6, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. C.","family":"ALEXANDER","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Case Western  Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106-7058, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00281500"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1977.26.26006"},{"key":"p_5","author":"Fiedler B.","year":"2000","journal-title":"SIAM J. Math. Anal., to appear."},{"key":"p_6","author":"Fiedler B.","year":"2000","journal-title":"J. Diff. Eqs., to appear."},{"key":"p_8","first-page":"191","volume":"99","author":"Levermore C. D.","year":"1996","journal-title":"Physica"},{"key":"p_9","first-page":"279","volume":"1","author":"Shoshitaishvili A. N.","year":"1975","journal-title":"Tr. Sem. Petrovskogo"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127400001018","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:40:11Z","timestamp":1565109611000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127400001018"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,7]]},"references-count":6,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2000,7]]}},"alternative-id":["10.1142\/S0218127400001018"],"URL":"https:\/\/doi.org\/10.1142\/s0218127400001018","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,7]]}}}