Dynamical systems analysis of a five-dimensional trophic food web model in the southern oceans
type: Item
instance of: scholarly article
title: Dynamical systems analysis of a five-dimensional trophic food web model in the southern oceans
zbMATH Open document ID: 1196.37125
DOI: 10.1155/2009/575047
author: Scott A. Hadley
author: Lawrence K. Forbes
published in: Journal of Applied Mathematics
publication date: 2010-04-14T00:00:00Z
full work available at URL: https://eudml.org/doc/233585
review text: The paper investigates the solutions of a dynamical system representing a theoretical model for a three-level trophic system in the ocean. The system consists of two distinct prey-predator networks, linked by competition for nutrients at the lowest level. There is also an interaction at the level of the two preys; the presence of one of the preys gives an advantage to the other one when nutrients are low. The model displays the interaction between phytoplankton, bacteria, zooplankton and nutrients. A particular emphasis in the analysis is on the stability of the steady-state populations and self-sustained solutions. Previous work on this model considered that the nutrient concentration was invariable, showing that the system becomes degenerate, in the sense that the unforced equations gave rise to equilibrium points that are centres. In this paper, the nutrient concentration is considered to be variable and, instead of degeneracy, Hopf bifurcation was observed for a range of parameter values. Using the Floquet theory, it is shown that the limit cycles change the stability as one moves along the solution branches. Some numerical results in \texttt{MATLAB} are presented at the end of the paper.
reviewed by: Iulian Stoleriu
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5692899
zbMATH Keywords: dynamical system
zbMATH Keywords: trophic food web model
zbMATH Keywords: prey-predator model
zbMATH Keywords: Floquet theory
Wikidata QID: Q58648641
describes a project that uses: Matlab
MaRDI profile type: Publication
OpenAlex ID: W2150145189
cites work: Zooplankton mortality and the dynamical behaviour of plankton population models
cites work: Q3994920
cites work: Stability and bifurcation behaviors analysis in a nonlinear harmful algal dynamical model
cites work: Q3992578
cites work: Forced Transverse Oscillations in a Simple Spring-Mass System
cites work: Practical bifurcation and stability analysis: from equilibrium to chaos.
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description: scientific article; zbMATH DE number 5692899