Please use this identifier to cite or link to this item: https://hdl.handle.net/10321/2302
Title: Identifying stability conditions and Hopf bifurcations in a consumer resource model using a consumption threshold
Authors: Duffy, Kevin Jan 
Collins, Obiora Cornelius 
Keywords: Consumer-resource model;Ecosystem dynamics;Stability analysis;Hopf bifurcation
Issue Date: 2016
Publisher: Elsevier
Source: Duffy, K.J. and Collins, O.C. 2016. Identifying stability conditions and Hopf bifurcations in a consumer resource model using a consumption threshold. Ecological Complexity. 28: 212-217.
Journal: Ecological modelling (Online) 
Abstract: 
The existence, or not, of cyclic dynamics is one of the pivotal aspects of ecological populations. This work considers a consumer resource model found in ecology that can describe both cyclic and non-cyclic dynamics depending on parameter conditions. A threshold consumption number C0 is introduced, similar to the basic reproduction in epidemiological models. It is shown that consumer survival requires C0 > 1 and that a Hopf bifurcation occurs at , where is defined here and is greater than 1. This result is discussed with an example and extensions to other more complicated models.
URI: http://hdl.handle.net/10321/2302
ISSN: 0304-3800 (print)
1872-7026 (online)
DOI: https://doi.org/10.1016/j.ecocom.2016.03.002
Appears in Collections:Research Publications (Systems Science)

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