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Two-spotted spider mite predator-prey model. (English) Zbl 1080.92062
Summary: This paper presents simulation models for the dynamics of a predator-prey system consisting of the two-spotted spider mite Tetranychus urticae Koch as a prey and its predator Phytoseiulus persimilis Athias-Henriot. The percentage infestation of plant has been used as a basic unit for population densities of prey and predators. Parameter estimation has been done with the inclusion of diffusion and time delays in the models. Initial ranges of parameter values have been chosen on the basis of biological information available through various publications. The parameters have been optimized by the best fit of calculated solutions to the field data. The models approximating biological field data have produced satisfactory results. Stability of the equilibria for each model has been investigated.

MSC:
92D40 Ecology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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