Dynamical systems analysis of a two-level trophic food web in the Southern Ocean

A theoretical model developed by Stone describing a two level trophic system in the Ocean is analyzed, for the case in which there is unlimited supply of nutrients. We show that spontaneous oscillations in population numbers are possible, but they do not arise from a Hopf bifurcation. Seasonal forci...

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Bibliographic Details
Published in:ANZIAM Journal
Main Authors: Hadley, SA, Forbes, LK
Format: Article in Journal/Newspaper
Language:English
Published: Cambridge University Press 2009
Subjects:
Mathematical Sciences
Applied Mathematics
Biological Mathematics
Southern Ocean
Online Access:https://doi.org/10.21914/anziamj.v50i0.1111
http://ecite.utas.edu.au/114269
id ftunivtasecite:oai:ecite.utas.edu.au:114269
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spelling ftunivtasecite:oai:ecite.utas.edu.au:114269 2023-05-15T18:25:04+02:00 Dynamical systems analysis of a two-level trophic food web in the Southern Ocean Hadley, SA Forbes, LK 2009 https://doi.org/10.21914/anziamj.v50i0.1111 http://ecite.utas.edu.au/114269 en eng Cambridge University Press http://dx.doi.org/10.21914/anziamj.v50i0.1111 Hadley, SA and Forbes, LK, Dynamical systems analysis of a two-level trophic food web in the Southern Ocean, ANZIAM Journal, 50 pp. E24-E55. ISSN 1446-8735 (2009) [Refereed Article] http://ecite.utas.edu.au/114269 Mathematical Sciences Applied Mathematics Biological Mathematics Refereed Article PeerReviewed 2009 ftunivtasecite https://doi.org/10.21914/anziamj.v50i0.1111 2019-12-13T22:14:11Z A theoretical model developed by Stone describing a two level trophic system in the Ocean is analyzed, for the case in which there is unlimited supply of nutrients. We show that spontaneous oscillations in population numbers are possible, but they do not arise from a Hopf bifurcation. Seasonal forcing of the model is also investigated, and it is shown that resonances can occur, in addition to highly non-linear behaviour including high period oscillations, quasi-periodicity and chaos. Article in Journal/Newspaper Southern Ocean eCite UTAS (University of Tasmania) Southern Ocean ANZIAM Journal 50 24
institution Open Polar
collection eCite UTAS (University of Tasmania)
op_collection_id ftunivtasecite
language English
topic Mathematical Sciences
Applied Mathematics
Biological Mathematics
spellingShingle Mathematical Sciences
Applied Mathematics
Biological Mathematics
Hadley, SA
Forbes, LK
Dynamical systems analysis of a two-level trophic food web in the Southern Ocean
topic_facet Mathematical Sciences
Applied Mathematics
Biological Mathematics
description A theoretical model developed by Stone describing a two level trophic system in the Ocean is analyzed, for the case in which there is unlimited supply of nutrients. We show that spontaneous oscillations in population numbers are possible, but they do not arise from a Hopf bifurcation. Seasonal forcing of the model is also investigated, and it is shown that resonances can occur, in addition to highly non-linear behaviour including high period oscillations, quasi-periodicity and chaos.
format Article in Journal/Newspaper
author Hadley, SA
Forbes, LK
author_facet Hadley, SA
Forbes, LK
author_sort Hadley, SA
title Dynamical systems analysis of a two-level trophic food web in the Southern Ocean
title_short Dynamical systems analysis of a two-level trophic food web in the Southern Ocean
title_full Dynamical systems analysis of a two-level trophic food web in the Southern Ocean
title_fullStr Dynamical systems analysis of a two-level trophic food web in the Southern Ocean
title_full_unstemmed Dynamical systems analysis of a two-level trophic food web in the Southern Ocean
title_sort dynamical systems analysis of a two-level trophic food web in the southern ocean
publisher Cambridge University Press
publishDate 2009
url https://doi.org/10.21914/anziamj.v50i0.1111
http://ecite.utas.edu.au/114269
geographic Southern Ocean
geographic_facet Southern Ocean
genre Southern Ocean
genre_facet Southern Ocean
op_relation http://dx.doi.org/10.21914/anziamj.v50i0.1111
Hadley, SA and Forbes, LK, Dynamical systems analysis of a two-level trophic food web in the Southern Ocean, ANZIAM Journal, 50 pp. E24-E55. ISSN 1446-8735 (2009) [Refereed Article]
http://ecite.utas.edu.au/114269
op_doi https://doi.org/10.21914/anziamj.v50i0.1111
container_title ANZIAM Journal
container_volume 50
container_start_page 24
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