caa a22 4500 477140610 CHVBK 20180405111731.0 cr unu---uuuuu 170330e19971101xx s 000 0 eng 10.1007/s002850050095 doi (NATIONALLICENCE)springer-10.1007/s002850050095 Collings John B. Mathematics Department, University of North Dakota, Grand Forks, ND 58202-8376, USA e-mail: collings@plains.nodak.edu, US aut The effects of the functional response on the bifurcation behavior of a mite predator-prey interaction model [Elektronische Daten] [John B. Collings] 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. Springer-Verlag Berlin Heidelberg, 1997 Key words: Predator nationallicence prey nationallicence Functional response nationallicence Bifurcation nationallicence Stability nationallicence https://doi.org/10.1007/s002850050095 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002850050095 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Collings John B. Mathematics Department, University of North Dakota, Grand Forks, ND 58202-8376, USA e-mail: collings@plains.nodak.edu, US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer