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Modeling on an ecological food chain with recycling
Cai, Qinghua2; Mohamad, Zakaria1; Yuan, Yuan1; Yuan, Y (reprint author), Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada.
2012-12-01
Source PublicationCOMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
ISSN1007-5704
Volume17Issue:12Pages:4856-4869
AbstractWe propose two nutrient-phytoplankton models with instantaneous and time delayed recycling, investigate the dynamics and examine the responses to model complexities. Instead of the familiar specific uptake rate and growth rate functions, we assume only that the nutrient uptake and phytoplankton growth rate functions are positive, increasing and bounded above. We use geometrical and analytical methods to find conditions for the existence of none, one, or at most two positive steady states and analyze the stability properties of each of these equilibria. With the variation of parameters, the system may lose its stability and bifurcation may occur. We study the occurrence of Hopf bifurcation and the possibility of stability switching. Numerical simulations illustrate the analytical results and provide further insight into the dynamics of the models, biological interpretations are given. (C) 2012 Elsevier B.V. All rights reserved.; We propose two nutrient-phytoplankton models with instantaneous and time delayed recycling, investigate the dynamics and examine the responses to model complexities. Instead of the familiar specific uptake rate and growth rate functions, we assume only that the nutrient uptake and phytoplankton growth rate functions are positive, increasing and bounded above. We use geometrical and analytical methods to find conditions for the existence of none, one, or at most two positive steady states and analyze the stability properties of each of these equilibria. With the variation of parameters, the system may lose its stability and bifurcation may occur. We study the occurrence of Hopf bifurcation and the possibility of stability switching. Numerical simulations illustrate the analytical results and provide further insight into the dynamics of the models, biological interpretations are given. (C) 2012 Elsevier B.V. All rights reserved.
SubtypeArticle
KeywordNutrient Phytoplankton Stability Hopf Bifurcation
Department[Mohamad, Zakaria; Yuan, Yuan] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada; [Cai, Qinghua] Chinese Acad Sci, Inst Hydrobiol, State Key Lab Freshwater Ecol & Biotechnol, Wuhan 430072, Peoples R China
DOI10.1016/j.cnsns.2012.04.022
WOS HeadingsScience & Technology ; Physical Sciences ; Technology
Funding OrganizationChinese Foundation; Natural Sciences and Engineering Research Council of Canada ; Chinese Foundation; Natural Sciences and Engineering Research Council of Canada ; Chinese Foundation; Natural Sciences and Engineering Research Council of Canada ; Chinese Foundation; Natural Sciences and Engineering Research Council of Canada
Indexed BySCI
Language英语
WOS Research AreaMathematics ; Mechanics ; Physics
WOS SubjectMathematics, Applied ; Mathematics, Interdisciplinary Applications ; Mechanics ; Physics, Fluids & Plasmas ; Physics, Mathematical
WOS IDWOS:000307104000038
WOS KeywordPHYTOPLANKTON BLOOMS ; COMPETITION ; NUTRIENT ; COEXISTENCE ; PERSISTENCE ; STABILITY ; ECOSYSTEM ; SYSTEM ; DELAY
Funding OrganizationChinese Foundation; Natural Sciences and Engineering Research Council of Canada ; Chinese Foundation; Natural Sciences and Engineering Research Council of Canada ; Chinese Foundation; Natural Sciences and Engineering Research Council of Canada ; Chinese Foundation; Natural Sciences and Engineering Research Council of Canada
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Document Type期刊论文
Identifierhttp://ir.ihb.ac.cn/handle/342005/17222
Collection淡水生态学研究中心_期刊论文
Corresponding AuthorYuan, Y (reprint author), Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada.
Affiliation1.Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
2.Chinese Acad Sci, Inst Hydrobiol, State Key Lab Freshwater Ecol & Biotechnol, Wuhan 430072, Peoples R China
Recommended Citation
GB/T 7714
Cai, Qinghua,Mohamad, Zakaria,Yuan, Yuan,et al. Modeling on an ecological food chain with recycling[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION,2012,17(12):4856-4869.
APA Cai, Qinghua,Mohamad, Zakaria,Yuan, Yuan,&Yuan, Y .(2012).Modeling on an ecological food chain with recycling.COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION,17(12),4856-4869.
MLA Cai, Qinghua,et al."Modeling on an ecological food chain with recycling".COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 17.12(2012):4856-4869.
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