{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T23:48:20Z","timestamp":1648511300087},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,3]]},"abstract":" In this paper we investigate the onset of instabilities in a model describing the propagation of the steady planar premixed combustion wave. In particular, we are interested in determining the Bogdanov\u2013Takens bifurcation condition, which is investigated semi-analytically. We derive an analytic condition for the existence of this type of bifurcation and based on this criterion we numerically determine the parameter values for which the Bogdanov\u2013Takens bifurcation occurs. This numerical method is found to be more efficient than the previous methods. <\/jats:p>","DOI":"10.1142\/s0218127406015131","type":"journal-article","created":{"date-parts":[[2006,5,23]],"date-time":"2006-05-23T11:19:24Z","timestamp":1148383164000},"page":"749-755","source":"Crossref","is-referenced-by-count":0,"title":["DETECTING BOGDANOV\u2013TAKENS BIFURCATION OF TRAVELING WAVES IN REACTION\u2013DIFFUSION SYSTEMS"],"prefix":"10.1142","volume":"16","author":[{"given":"V. V.","family":"GUBERNOV","sequence":"first","affiliation":[{"name":"International Laser Center, M.V. Lomonosov Moscow State University, Moscow 119899, Russia"},{"name":"I.E. Tamm Theory Department, P.N. Lebedev Physical Institute, Russian Academy of Science, 53, Leninskii Prospect, Moscow 119991, Russia"}]},{"given":"H. S.","family":"SIDHU","sequence":"additional","affiliation":[{"name":"School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600, Australia"}]},{"given":"G. N.","family":"MERCER","sequence":"additional","affiliation":[{"name":"School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600, Australia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1088\/1364-7830\/5\/3\/304"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/0147084"},{"key":"rf3","first-page":"1259","volume":"63","author":"Gubernov V.","journal-title":"SIAM J. Appl. Math."},{"key":"rf4","first-page":"1259","volume":"460","author":"Gubernov V.","journal-title":"Proc. R. Soc. Lond. A"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0010-2180(79)90018-X"},{"key":"rf6","volume-title":"Elements of Applied Bifurcation Theory","author":"Kuznetsov Y. A.","year":"1998"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0246"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0076-5392(08)62388-7"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01031343"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127406015131","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:10:22Z","timestamp":1565136622000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127406015131"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3]]},"references-count":9,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,3]]}},"alternative-id":["10.1142\/S0218127406015131"],"URL":"https:\/\/doi.org\/10.1142\/s0218127406015131","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,3]]}}}