{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:37:25Z","timestamp":1772293045944,"version":"3.50.1"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> This paper is devoted to the study of an age-dependent population system with Riker type birth function. The time lag factor is considered for the birth process. We investigate some dynamical properties of the equation by using C<jats:sub>0<\/jats:sub>-semigroup theory, through which we obtain some conditions of asymptotical stability and Hopf bifurcation occurring at positive steady state for the system. <\/jats:p>","DOI":"10.1142\/s0218127412501465","type":"journal-article","created":{"date-parts":[[2012,4,24]],"date-time":"2012-04-24T01:04:26Z","timestamp":1335229466000},"page":"1250146","source":"Crossref","is-referenced-by-count":5,"title":["HOPF BIFURCATION IN AN AGE-DEPENDENT POPULATION MODEL WITH DELAYED BIRTH PROCESS"],"prefix":"10.1142","volume":"22","author":[{"given":"PING","family":"BI","sequence":"first","affiliation":[{"name":"Department of Mathematics, East China Normal University, Shanghai 200241, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"XIANLONG","family":"FU","sequence":"additional","affiliation":[{"name":"Department of Mathematics, East China Normal University, Shanghai 200241, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,7,16]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/080742713"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/9.679018"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9436-3"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0016-0032(74)90039-8"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.04.003"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF00163023"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970005"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.09.074"},{"key":"rf9","series-title":"Graduate Texts in Mathematics","volume-title":"One-Parameter Semigroups for Linear Evolution Equations","volume":"194","author":"Engel K.-J.","year":"2000"},{"key":"rf10","first-page":"249","volume":"9","author":"Farkas J. Z.","journal-title":"Discr. Contin. Dyn. Syst. Ser. B"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2003.08.047"},{"key":"rf12","first-page":"735","volume":"7","author":"Fragnelli G.","journal-title":"Discr. Cont. Dyn. Syst. B"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0072769"},{"key":"rf14","series-title":"London Math. Soc. Lect. Note Ser","volume-title":"Theory and Applications of Hopf Bifurcaton","volume":"41","author":"Hassard B.","year":"1981"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/BF00161518"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02807217"},{"key":"rf17","first-page":"197","volume":"20","author":"Magal P.","journal-title":"Diff. Int. Eq."},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-008-9127-0"},{"key":"rf19","volume":"202","author":"Magal P.","journal-title":"Mem. Amer. Math. Soc."},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0435"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-13159-6"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(90)90096-4"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1002\/mma.462"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-004-0159-6"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1139\/f54-039"},{"key":"rf27","first-page":"1","volume":"191","author":"Ricker W. E.","journal-title":"Bull. Fish. Res. Board Can."},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-010-0381-5"},{"key":"rf29","volume-title":"Theory of Nonlinear Age-Dependent Population Dynamics","author":"Webb G. F.","year":"1985"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1137\/090777645"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127412501465","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:32:39Z","timestamp":1565112759000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127412501465"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":30,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2012,7,16]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1142\/S0218127412501465"],"URL":"https:\/\/doi.org\/10.1142\/s0218127412501465","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}