Stabilization due to predator interference: comparison of different analysis approaches
We study the influence of the particular form of the functionalresponse in two-dimensional predator-prey models with respect to the stabilityof the nontrivial equilibrium. This equilibrium is stable between its appearanceat a transcritical bifurcation and its destabilization at a Hopf bifurcation,gi...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2008-05-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.567 |
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| Summary: | We study the influence of the particular form of the functionalresponse in two-dimensional predator-prey models with respect to the stabilityof the nontrivial equilibrium. This equilibrium is stable between its appearanceat a transcritical bifurcation and its destabilization at a Hopf bifurcation,giving rise to periodic behavior. Based on local bifurcation analysis, we introducea classification of stabilizing effects. The classical Rosenzweig-MacArthurmodel can be classified as weakly stabilizing, undergoing the paradox of enrichment,while the well known Beddington-DeAngelis model can be classifiedas strongly stabilizing. Under certain conditions we obtain a completestabilization, resulting in an avoidance of limit cycles. Both models, in theirconventional formulation, are compared to a generalized, steady-state independenttwo-dimensional version of these models, based on a previously developednormalization method. We show explicitly how conventional and generalizedmodels are related and how to interpret the results from the rather abstractstability analysis of generalized models. |
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| ISSN: | 1551-0018 |