Bulletin of Mathematical Biology

, Volume 57, Issue 1, pp 63–76

Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge

  • John B. Collings


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.


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Copyright information

© Society for Mathematical Biology 1994

Authors and Affiliations

  • John B. Collings
    • 1
  1. 1.Mathematics DepartmentUniversity of North DakotaGrand ForksUSA

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