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|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.||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 R0 in epidemiological models. It is shown that consumer survival requires C0 > 1 and that a Hopf bifurcation occurs at C0 ¼ C, where C 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)
|Appears in Collections:||Research Publications (Systems Science)|
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