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  • 1995-1999  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 63-76 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The non-linear behavior of a differential equations-based predator-prey model, incorporating a spatial refuge protecting a consant proportion of prey and with temperature-dependent parameters chosen appropriately for a mite interaction on fruit trees, is examined using the numerical bifurcation code AUTO 86. The most significant result of this analysis is the existence of a temperature interval in which increasing the amount of refuge dynamically destabilizes the system; and on part of this interval the interaction is less likely to persist in that predator and prey minimum population densities are lower than when no refuge is available. It is also shown that increasing the amount of refuge can lead to population outbreaks due to the presence of multiple stable states. The ecological implications of a refuge are discussed with respect to the biological control of mite pests.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458316
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  • 2
    Electronic Resource
    Electronic Resource
    The effects of the functional response on the bifurcation behavior of a mite predator–prey interaction model (1997)
    Springer
    Journal of mathematical biology 36 (1997), S. 149-168 
    Details
    ISSN: 1432-1416
    Keywords: Key words: Predator ; prey ; Functional response ; Bifurcation ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002850050095
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    Paper (German National Licenses)
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