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Product No. 99764 Supplementary Print Price: FREE with membership
 

Of Mites and Models: A Temperature-Dependent Model of a Mite Predator-Prey Interaction (UMAP)

John B. Collings and David J. Wollkind


Mathematics Topic:
Differential Equations, Modeling
Application Areas:
Population biology
Prerequisites:
Familiarity with the qualitative analysis of systems of differential equations (phase-plane analysis)

| ©1998 by COMAP, Inc. | The UMAP Journal 19.1 | 22 pages |


This module analyzes the qualitative behavior of a model for a mite predator-prey interaction. This model is based on a simple system of differential equations, and the model parameters are assigned values determined for a specific interaction between two species of mites. Several of these parameters are functions of temperature, and temperature is treated as a bifurcation parameter in the analysis of the model. It is shown that, depending on the temperature value, the model exhibits a stable fixed point, a stable limit cycle, or both (bistability). The model is used to illustrate population outbreaks.

Table of Contents:

INTRODUCTION

DEVELOPMENT OF THE MODEL

ANALYSIS OF THE MODEL, PART I

ANALYSIS OF THE MODEL, PART II

SOFTWARE NOTES

SOLUTIONS TO THE EXERCISES

REFERENCES

ABOUT THE AUTHORS