{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T05:28:59Z","timestamp":1768454939938,"version":"3.49.0"},"reference-count":10,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T00:00:00Z","timestamp":1627776000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T00:00:00Z","timestamp":1627776000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"vor","delay-in-days":1461,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"},{"start":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T00:00:00Z","timestamp":1627776000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T00:00:00Z","timestamp":1627776000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T00:00:00Z","timestamp":1627776000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T00:00:00Z","timestamp":1627776000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T00:00:00Z","timestamp":1627776000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671260"],"award-info":[{"award-number":["11671260"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071293"],"award-info":[{"award-number":["12071293"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics Letters"],"published-print":{"date-parts":[[2021,8]]},"DOI":"10.1016\/j.aml.2021.107146","type":"journal-article","created":{"date-parts":[[2021,2,27]],"date-time":"2021-02-27T04:45:14Z","timestamp":1614401114000},"page":"107146","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":22,"special_numbering":"C","title":["Dynamics of a toxic producing phytoplankton\u2013zooplankton model with three\u2013dimensional patch"],"prefix":"10.1016","volume":"118","author":[{"given":"Jingen","family":"Yang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0502-3653","authenticated-orcid":false,"given":"Sanling","family":"Yuan","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.aml.2021.107146_b1","series-title":"Estimated Annual Economic Impacts from Harmful Algal Blooms (HABs) in the United States","author":"Anderson","year":"2000"},{"issue":"3","key":"10.1016\/j.aml.2021.107146_b2","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.dsr.2006.12.005","article-title":"Mechanisms determining species dominance in a phytoplankton bloom induced by the iron fertilization experiment EisenEx in the Southern Ocean","volume":"54","author":"Assmy","year":"2007","journal-title":"Deep Sea Res. I"},{"key":"10.1016\/j.aml.2021.107146_b3","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.nahs.2019.06.005","article-title":"Asymptotic properties of stochastic nutrient-plankton food chain models with nutrient recycling","volume":"34","author":"Yu","year":"2019","journal-title":"Nonlinear Anal. Hybrid Syst."},{"issue":"5","key":"10.1016\/j.aml.2021.107146_b4","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s11538-020-00733-y","article-title":"Noise-induced transitions in a nonsmooth producer-grazer model with stoichiometric constraints","volume":"82","author":"Yuan","year":"2020","journal-title":"Bull. Math. Biol."},{"key":"10.1016\/j.aml.2021.107146_b5","series-title":"Allelopathy","author":"Rice","year":"1984"},{"issue":"2","key":"10.1016\/j.aml.2021.107146_b6","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.jtbi.2008.03.008","article-title":"Patchy agglomeration as a transition from monospecies to recurrent plankton blooms","volume":"253","author":"Chattopadhyay","year":"2008","journal-title":"J. Theoret. Biol."},{"issue":"4","key":"10.1016\/j.aml.2021.107146_b7","doi-asserted-by":"crossref","DOI":"10.1142\/S0218127419300118","article-title":"Pattern dynamics of a diffusive toxin producing phytoplankton-zooplankton model with three-dimensional patch","volume":"29","author":"Jia","year":"2019","journal-title":"Int. J. Bifurcation Chaos"},{"key":"10.1016\/j.aml.2021.107146_b8","series-title":"Differential Equations and Dynamical Systems","author":"Perko","year":"1996"},{"key":"10.1016\/j.aml.2021.107146_b9","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.nonrwa.2016.05.010","article-title":"Stability and bifurcation analysis in a predator-prey system with Michaelis-Menten type predator harvesting","volume":"33","author":"Hu","year":"2017","journal-title":"Nonlinear Anal. Real World Appl."},{"issue":"4","key":"10.1016\/j.aml.2021.107146_b10","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1137\/S0036139999361896","article-title":"Global analysis in a predator-prey system with nonmonotonic functional response","volume":"61","author":"Ruan","year":"2001","journal-title":"SIAM J. Appl. Math."}],"container-title":["Applied Mathematics Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965921000720?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965921000720?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:54:57Z","timestamp":1760241297000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893965921000720"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8]]},"references-count":10,"alternative-id":["S0893965921000720"],"URL":"https:\/\/doi.org\/10.1016\/j.aml.2021.107146","relation":{},"ISSN":["0893-9659"],"issn-type":[{"value":"0893-9659","type":"print"}],"subject":[],"published":{"date-parts":[[2021,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Dynamics of a toxic producing phytoplankton\u2013zooplankton model with three\u2013dimensional patch","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics Letters","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.aml.2021.107146","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2021 Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"107146"}}