The effects of the functional response on the bifurcation behavior of a mite predator–prey interaction model |
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Authors: | John B Collings |
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Institution: | (1) Mathematics Department, University of North Dakota, Grand Forks, ND 58202-8376, USA e-mail: collings@plains.nodak.edu, US |
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Abstract: | A predator–prey interaction model based on a system of differential equations with temperature-dependent parameters chosen
appropriately for a mite interaction on apple trees is analyzed to determine how the type of functional response influences
bifurcation and stability behavior. Instances of type I, II, III, and IV functional responses are considered, the last of
which incorporates prey interference with predation. It is shown that the model systems with the type I, II, and III functional
responses exhibit qualitatively similar bifurcation and stability behavior over the interval of definition of the temperature
parameter. Similar behavior is found in the system with the type IV functional response at low levels of prey interference.
Higher levels of interference are destabilizing, as illustrated by the prevalence of bistability and by the presence of three
attractors for some values of the model parameters. All four systems are capable of modeling population oscillations and outbreaks.
Received 12 March 1996; received in revised form 25 October 1996 |
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Keywords: | : Predator prey Functional response Bifurcation Stability |
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