{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:52:50Z","timestamp":1760889170537,"version":"3.37.3"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (CN)","doi-asserted-by":"publisher","award":["11371111"],"award-info":[{"award-number":["11371111"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013286","name":"Research Fund for the Doctoral Program of Higher Education of China","doi-asserted-by":"crossref","award":["20122302110044"],"award-info":[{"award-number":["20122302110044"]}],"id":[{"id":"10.13039\/501100013286","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Scientific Research Fund of Heilongjiang Provincial Education Department","award":["12541893"],"award-info":[{"award-number":["12541893"]}]},{"name":"Program for Young Teachers Scientific Research in Qiqihar University","award":["2012k-M28"],"award-info":[{"award-number":["2012k-M28"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,3]]},"abstract":"<jats:p> A reaction\u2013diffusion plankton system with delay and quadratic closure term is investigated to study the interactions between phytoplankton and zooplankton. Sufficient conditions independent of diffusion and delay are obtained for the persistence of the system. Our conclusions show that diffusion can induce Turing instability, delay can influence the stability of the positive equilibrium and induce Hopf bifurcations to occur. The computational formulas which determine the properties of bifurcating periodic solutions are given by calculating the normal form on the center manifold, and some numerical simulations are carried out for illustrating the theoretical results. <\/jats:p>","DOI":"10.1142\/s0218127416500474","type":"journal-article","created":{"date-parts":[[2016,4,5]],"date-time":"2016-04-05T23:23:16Z","timestamp":1459898596000},"page":"1650047","source":"Crossref","is-referenced-by-count":9,"title":["Persistence, Turing Instability and Hopf Bifurcation in a Diffusive Plankton System with Delay and Quadratic Closure"],"prefix":"10.1142","volume":"26","author":[{"given":"Jiantao","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, P. R. China"},{"name":"Department of Mathematics, Qiqihar University, Qiqihar, Heilongjiang 161006, P. R. China"}]},{"given":"Junjie","family":"Wei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2016,4,5]]},"reference":[{"key":"S0218127416500474BIB001","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7381"},{"key":"S0218127416500474BIB002","doi-asserted-by":"publisher","DOI":"10.1093\/plankt\/20.9.1837"},{"key":"S0218127416500474BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2015.03.010"},{"key":"S0218127416500474BIB004","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2013.12.481"},{"key":"S0218127416500474BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-008-0221-6"},{"key":"S0218127416500474BIB006","doi-asserted-by":"publisher","DOI":"10.1006\/bulm.1998.0082"},{"key":"S0218127416500474BIB007","doi-asserted-by":"publisher","DOI":"10.1093\/plankt\/22.6.1085"},{"key":"S0218127416500474BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(00)00065-5"},{"key":"S0218127416500474BIB009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-00-02280-7"},{"key":"S0218127416500474BIB010","doi-asserted-by":"publisher","DOI":"10.1357\/002224090784984678"},{"key":"S0218127416500474BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.02.048"},{"key":"S0218127416500474BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(02)00494-0"},{"volume-title":"Theory and Applications of Hopf Bifurcation","year":"1981","author":"Hassard B.","key":"S0218127416500474BIB013"},{"key":"S0218127416500474BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.11.052"},{"key":"S0218127416500474BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413500235"},{"key":"S0218127416500474BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(99)00393-4"},{"key":"S0218127416500474BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecolmodel.2008.12.008"},{"key":"S0218127416500474BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413501745"},{"key":"S0218127416500474BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(00)00189-9"},{"key":"S0218127416500474BIB020","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/61.1.15"},{"key":"S0218127416500474BIB021","first-page":"863","volume":"10","author":"Ruan S.","year":"2003","journal-title":"Dyn. Contin. Discr. Impuls. Syst., Ser. A: Math. Anal."},{"key":"S0218127416500474BIB022","first-page":"1530014-1","volume":"25","author":"Shi H.","year":"2015","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S0218127416500474BIB023","doi-asserted-by":"publisher","DOI":"10.1142\/S021812741450093X"},{"key":"S0218127416500474BIB024","doi-asserted-by":"publisher","DOI":"10.1086\/283752"},{"key":"S0218127416500474BIB025","doi-asserted-by":"publisher","DOI":"10.1093\/plankt\/14.1.157"},{"key":"S0218127416500474BIB026","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411028684"},{"key":"S0218127416500474BIB027","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4050-1"},{"key":"S0218127416500474BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.12.016"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127416500474","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T18:26:36Z","timestamp":1569954396000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127416500474"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3]]},"references-count":28,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2016,4,5]]},"published-print":{"date-parts":[[2016,3]]}},"alternative-id":["10.1142\/S0218127416500474"],"URL":"https:\/\/doi.org\/10.1142\/s0218127416500474","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2016,3]]}}}