{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:43:48Z","timestamp":1740120228049,"version":"3.37.3"},"reference-count":38,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100001809","name":"NSF of China","doi-asserted-by":"crossref","award":["11371087"],"award-info":[{"award-number":["11371087"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003399","name":"STCSM","doi-asserted-by":"crossref","award":["13dz2260400"],"award-info":[{"award-number":["13dz2260400"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012150","name":"Shanghai Leading Academic Discipline Project","doi-asserted-by":"crossref","award":["B407"],"award-info":[{"award-number":["B407"]}],"id":[{"id":"10.13039\/501100012150","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,3]]},"abstract":"<jats:p> This paper is devoted to the study of a spatially and size-structured population dynamics model with delay in the birth process. We investigate some dynamical properties of the equation by using [Formula: see text]-semigroup theory and spectral analysis arguments, through which we obtain some sufficient conditions of asymptotical stability, asynchronous exponential growth at the null equilibrium as well as Hopf bifurcation occurring at the positive steady state of the system. Some examples are presented and simulated to illustrate the obtained results. <\/jats:p>","DOI":"10.1142\/s0218127417500328","type":"journal-article","created":{"date-parts":[[2017,4,10]],"date-time":"2017-04-10T00:15:00Z","timestamp":1491783300000},"page":"1750032","source":"Crossref","is-referenced-by-count":4,"title":["Long-Time Behavior of Spatially and Size-Structured Population Dynamics with Delayed Birth Process"],"prefix":"10.1142","volume":"27","author":[{"given":"Dongxue","family":"Yan","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":[[2017,4,9]]},"reference":[{"key":"S0218127417500328BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0016-0032(74)90039-8"},{"key":"S0218127417500328BIB002","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2001.6705"},{"key":"S0218127417500328BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412501465"},{"key":"S0218127417500328BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-011-0100-8"},{"key":"S0218127417500328BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.04.003"},{"key":"S0218127417500328BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(79)90073-7"},{"key":"S0218127417500328BIB007","doi-asserted-by":"publisher","DOI":"10.1137\/060659211"},{"key":"S0218127417500328BIB008","first-page":"187","volume":"47","author":"Diekmann O.","year":"2008","journal-title":"Funct. Anal. Evol. Eqs."},{"key":"S0218127417500328BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2010.09.019"},{"key":"S0218127417500328BIB010","first-page":"373","volume":"1","author":"Ducrot A.","year":"2011","journal-title":"J. Appl. Anal. Comput."},{"key":"S0218127417500328BIB011","first-page":"61","volume":"966","author":"Engel K. J.","year":"1996","journal-title":"RIMS Kokyuroku"},{"volume-title":"One-Parameter Semigroups for Linear Evolution Equations","year":"2000","author":"Engel K. J.","key":"S0218127417500328BIB012"},{"key":"S0218127417500328BIB013","first-page":"109","volume":"1","author":"Fu X.","year":"2013","journal-title":"Discr. Cont. Dyn. Syst. B"},{"key":"S0218127417500328BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0072769"},{"key":"S0218127417500328BIB015","first-page":"213","volume":"13","author":"Greiner G.","year":"1987","journal-title":"Houston J. Math."},{"key":"S0218127417500328BIB016","doi-asserted-by":"publisher","DOI":"10.1080\/03605308908820630"},{"key":"S0218127417500328BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(92)90218-3"},{"key":"S0218127417500328BIB018","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1999.6708"},{"key":"S0218127417500328BIB019","first-page":"19","volume":"14","author":"Hagen T.","year":"2001","journal-title":"Diff. Integer. Eqs."},{"key":"S0218127417500328BIB020","series-title":"London Math. Soc. Lect. Note Ser.","volume-title":"Theory and Applications of Hopf Bifurcaton","volume":"41","author":"Hassard B. D.","year":"1981"},{"key":"S0218127417500328BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-010-0088-x"},{"key":"S0218127417500328BIB022","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2015.20.1735"},{"key":"S0218127417500328BIB023","volume":"951","author":"Magal P.","year":"2009","journal-title":"Mem. Amer. Math. Soc."},{"key":"S0218127417500328BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0074922"},{"key":"S0218127417500328BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(90)90096-4"},{"key":"S0218127417500328BIB026","doi-asserted-by":"publisher","DOI":"10.1080\/16073606.1996.9631827"},{"key":"S0218127417500328BIB027","first-page":"207","volume":"4","author":"Nickel G.","year":"1994","journal-title":"Tu\u00fcbinger Berichte zur Funktionalanalysis"},{"key":"S0218127417500328BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"S0218127417500328BIB029","doi-asserted-by":"publisher","DOI":"10.1002\/mma.462"},{"key":"S0218127417500328BIB030","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-004-0159-6"},{"key":"S0218127417500328BIB031","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.1999.5.663"},{"key":"S0218127417500328BIB032","doi-asserted-by":"publisher","DOI":"10.1139\/f54-039"},{"key":"S0218127417500328BIB033","volume":"191","author":"Ricker W. E.","year":"1975","journal-title":"Bull. Fish. Res. Board Can."},{"key":"S0218127417500328BIB034","doi-asserted-by":"publisher","DOI":"10.1137\/0132040"},{"key":"S0218127417500328BIB035","doi-asserted-by":"publisher","DOI":"10.1137\/0511080"},{"key":"S0218127417500328BIB036","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-010-0381-5"},{"key":"S0218127417500328BIB037","first-page":"1035","volume":"3","author":"Thieme H. R.","year":"1990","journal-title":"Diff. Integr. Eqs."},{"volume-title":"Theory of Nonlinear Age-Dependent Population Dynamics","year":"1985","author":"Webb G. F.","key":"S0218127417500328BIB038"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417500328","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T09:41:39Z","timestamp":1565084499000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417500328"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3]]},"references-count":38,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2017,4,9]]},"published-print":{"date-parts":[[2017,3]]}},"alternative-id":["10.1142\/S0218127417500328"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417500328","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2017,3]]}}}