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We analyze the existence of the\nradially symmetric solutions and the occurrence of Hopf bifurcation as a parameter varies in two and\nthree\u2010dimensional spaces.<\/jats:p>","DOI":"10.1155\/2010\/529869","type":"journal-article","created":{"date-parts":[[2010,11,29]],"date-time":"2010-11-29T19:35:56Z","timestamp":1291059356000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hopf Bifurcation with the Spatial Average of an Activator in a Radially Symmetric Free Boundary Problem"],"prefix":"10.1155","volume":"2010","author":[{"given":"YoonMee","family":"Ham","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,11,29]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0378\u20104371(00)00636\u20101"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.440418"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.63.106"},{"volume-title":"Models of Biological Pattern Formulation","year":"1982","author":"Meinhardt H.","key":"e_1_2_6_4_2"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.02.019"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.02.020"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.42.7426"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.52.3645"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.63.1152"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1952.0012"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.57.2640"},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.62.1778"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s002570050419"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s100510050019"},{"key":"e_1_2_6_15_2","doi-asserted-by":"publisher","DOI":"10.1137\/0149029"},{"key":"e_1_2_6_16_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.42.3225"},{"key":"e_1_2_6_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377\u20100427(94)90363\u20108"},{"key":"e_1_2_6_18_2","doi-asserted-by":"publisher","DOI":"10.1137\/0511057"},{"key":"e_1_2_6_19_2","doi-asserted-by":"publisher","DOI":"10.1137\/0518124"},{"key":"e_1_2_6_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/0378\u20104371(96)00051\u20109"},{"key":"e_1_2_6_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167\u20102789(89)90230\u20103"},{"key":"e_1_2_6_22_2","doi-asserted-by":"publisher","DOI":"10.1137\/0146062"},{"key":"e_1_2_6_23_2","doi-asserted-by":"crossref","first-page":"173","DOI":"10.4310\/DPDE.2008.v5.n2.a4","article-title":"A Hopf bifurcation in a radially symmetric free boundary problem","volume":"5","author":"Lee S.-G.","year":"2008","journal-title":"Dynamics of Partial Differential Equations"},{"key":"e_1_2_6_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0089647"}],"container-title":["Mathematical Problems in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/mpe\/2010\/529869.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/mpe\/2010\/529869.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2010\/529869","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T06:19:04Z","timestamp":1718950744000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2010\/529869"}},"subtitle":[],"editor":[{"given":"Oded","family":"Gottlieb","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1155\/2010\/529869"],"URL":"https:\/\/doi.org\/10.1155\/2010\/529869","archive":["Portico"],"relation":{},"ISSN":["1024-123X","1563-5147"],"issn-type":[{"type":"print","value":"1024-123X"},{"type":"electronic","value":"1563-5147"}],"subject":[],"published":{"date-parts":[[2010,1]]},"assertion":[{"value":"2010-08-05","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-10-21","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-11-29","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"529869"}}