Mathematical analysis of a model for a plant-herbivore system

Linda J.S. Allen; Mary K. Hannigan; Monty J. Strauss

doi:10.1007/BF02460676

Mathematical analysis of a model for a plant-herbivore system

Linda J.S. Allen, Mary K. Hannigan, Monty J. Strauss

Mathematics and Statistics

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13 Scopus citations

Abstract

The apple twig borer (Amphicerus bicaudatus) is an insect pest of the grape vine, causing considerable damage to the grape vine in early spring. A simple difference equation model is formulated and analysed for this plant-herbivore system based on two control strategies, cane removal and pesticide application. The system has two equilibria, one where the pest is present and one where the pest is absent. Regions are found in parameter space for global stability of the equilibria and in the absence of global stability it is shown that there exist periodic or quasiperiodic solutions.

Original language	English
Pages (from-to)	847-864
Number of pages	18
Journal	Bulletin of Mathematical Biology
Volume	55
Issue number	4
DOIs	https://doi.org/10.1007/BF02460676
State	Published - Jul 1993

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abstract = "The apple twig borer (Amphicerus bicaudatus) is an insect pest of the grape vine, causing considerable damage to the grape vine in early spring. A simple difference equation model is formulated and analysed for this plant-herbivore system based on two control strategies, cane removal and pesticide application. The system has two equilibria, one where the pest is present and one where the pest is absent. Regions are found in parameter space for global stability of the equilibria and in the absence of global stability it is shown that there exist periodic or quasiperiodic solutions.",

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AB - The apple twig borer (Amphicerus bicaudatus) is an insect pest of the grape vine, causing considerable damage to the grape vine in early spring. A simple difference equation model is formulated and analysed for this plant-herbivore system based on two control strategies, cane removal and pesticide application. The system has two equilibria, one where the pest is present and one where the pest is absent. Regions are found in parameter space for global stability of the equilibria and in the absence of global stability it is shown that there exist periodic or quasiperiodic solutions.

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