title: Stabilization due to predator interference: comparison of different analysis approaches.
abstract: We study the influence of the particular form of the functional response in two-dimensional predator-prey models with respect to the stability of the nontrivial equilibrium. This equilibrium is stable between its appearance at a transcritical bifurcation and its destabilization at a Hopf bifurcation, giving rise to periodic behavior. Based on local bifurcation analysis, we introduce a classification of stabilizing effects. The classical Rosenzweig-MacArthur model can be classified as weakly stabilizing, undergoing the paradox of enrichment, while the well known Beddington-DeAngelis model can be classified as strongly stabilizing. Under certain conditions we obtain a complete stabilization, resulting in an avoidance of limit cycles. Both models, in their conventional formulation, are compared to a generalized, steady-state independent two-dimensional version of these models, based on a previously developed normalization method. We show explicitly how conventional and generalized models are related and how to interpret the results from the rather abstract stability analysis of generalized models.
authors.affiliation: Dept. Theor. Biology, Vrije Universiteit, de Boelelaan 1087, 1081 HV Amsterdam, The Netherlands. george.van.voorn@falw.vu.nl.
authors.forename: G A K
authors.initials: GA
authors.lastname: van Voorn
authors.forename: D
authors.initials: D
authors.lastname: Stiefs
authors.forename: T
authors.initials: T
authors.lastname: Gross
authors.forename: B W
authors.initials: BW
authors.lastname: Kooi
authors.forename: U
authors.initials: U
authors.lastname: Feudel
authors.forename: S A L M
authors.initials: SA
authors.lastname: Kooijman
mesh_terms: D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D020387:Food Chain; D008433:Mathematics; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D011157:Population Dynamics; D011235:Predatory Behavior