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Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate
Ren, Jingli; Yuan, Qigang; Ren, JL (reprint author), Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China.; Ren, JL (reprint author), Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China.
Source PublicationCHAOS
2017-08-01
Volume27Issue:8
ISSN1054-1500
AbstractA three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincare map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincare map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last. Published by AIP Publishing.
DOI10.1063/1.5000152
URL查看原文
Indexed BySCI
Language英语
WOS IDWOS:000409112600028
WOS KeywordNONLINEAR DYNAMICAL-SYSTEM ; GLYCEROL FERMENTATION ; KLEBSIELLA-PNEUMONIAE ; CLOSTRIDIUM-BUTYRICUM ; PRODUCT INHIBITION ; 1,3-PROPANEDIOL ; PATHWAY ; OSCILLATIONS ; HYSTERESIS
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
Funding OrganizationNSFC(11771407) ; Innovation Research Team of Science and Technology of Henan Province(17IRTSTHN007) ; Plan for Scientific Innovation Talent of Henan Province(164200510011) ; Opening fund of State Key Laboratory of Nonlinear Mechanics(LNM201710) ; National Key Research and Development Program of China(2017YFB0702500)
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Ranking2
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Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/70042
Collection非线性力学国家重点实验室
Corresponding AuthorRen, JL (reprint author), Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China.; Ren, JL (reprint author), Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China.
Recommended Citation
GB/T 7714
Ren, Jingli,Yuan, Qigang,Ren, JL ,et al. Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate[J]. CHAOS,2017,27(8).
APA Ren, Jingli,Yuan, Qigang,Ren, JL ,&Ren, JL .(2017).Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate.CHAOS,27(8).
MLA Ren, Jingli,et al."Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate".CHAOS 27.8(2017).
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