Bifurcations for a phytoplankton model with time delay

Bifurcations for a phytoplankton model with time delay

Applying a frequency domain approach, we investigate a phytoplankton model with time delay. We use the delay as a bifurcation parameter; as it passes through a sequence of critical values, Hopf bifurcation occurs. A family of periodic solutions bifurcate from the equilibrium when the bifurcatio...

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Bibliographic Details
Main Author: Changjin Xu
Format: Article
Language:English
Published: Texas State University 2011-11-01
Series:Electronic Journal of Differential Equations
Subjects:
Phytoplankton model
Hopf bifurcation
stability
frequency domain
Nyquist criterion
Online Access:http://ejde.math.txstate.edu/Volumes/2011/148/abstr.html
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spelling doaj-de5427b24755489fa3c4299b0f51857d2020-11-24T22:25:35ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-11-012011148,18Bifurcations for a phytoplankton model with time delayChangjin XuApplying a frequency domain approach, we investigate a phytoplankton model with time delay. We use the delay as a bifurcation parameter; as it passes through a sequence of critical values, Hopf bifurcation occurs. A family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations illustrate our theoretical results. http://ejde.math.txstate.edu/Volumes/2011/148/abstr.htmlPhytoplankton modelHopf bifurcationstabilityfrequency domainNyquist criterion
collection DOAJ
language English
format Article
sources DOAJ
author Changjin Xu
spellingShingle Changjin Xu
Bifurcations for a phytoplankton model with time delay
Electronic Journal of Differential Equations
Phytoplankton model
Hopf bifurcation
stability
frequency domain
Nyquist criterion
author_facet Changjin Xu
author_sort Changjin Xu
title Bifurcations for a phytoplankton model with time delay
title_short Bifurcations for a phytoplankton model with time delay
title_full Bifurcations for a phytoplankton model with time delay
title_fullStr Bifurcations for a phytoplankton model with time delay
title_full_unstemmed Bifurcations for a phytoplankton model with time delay
title_sort bifurcations for a phytoplankton model with time delay
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2011-11-01
description Applying a frequency domain approach, we investigate a phytoplankton model with time delay. We use the delay as a bifurcation parameter; as it passes through a sequence of critical values, Hopf bifurcation occurs. A family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations illustrate our theoretical results.
topic Phytoplankton model
Hopf bifurcation
stability
frequency domain
Nyquist criterion
url http://ejde.math.txstate.edu/Volumes/2011/148/abstr.html
work_keys_str_mv AT changjinxu bifurcationsforaphytoplanktonmodelwithtimedelay
_version_ 1725756777346105344

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