The apple twig borer (Amphicerus bicaudatus) is an insect pest of the
grape vine, causing considerable damage to the grape vine in early spr
ing. A simple difference equation model is formulated and analysed for
this plant-herbivore system based on two control strategies, cane rem
oval and pesticide application. The system has two equilibria, one whe
re the pest is present and one where the pest is absent. Regions are f
ound 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.