ABSTRACT
Dynamical systems models are amenable to a variety of useful mathematical analyses and optimization techniques so that the long-term stability of the modeled agricultural ecosystems may be completely understood and so that the model may explicitly focus on optimizing farm management. The process of formulating a prototype model describing the dynamic interactions between pasture mass and liveweight gain by grazing animals. The chapter reviews mathematical models that have been used to analyze agricultural grazing systems management. It returns to the pasture mass-liveweight gain model to illustrate how a qualitative analysis of the system stability is carried out through phase plane analysis. The chapter considers an example of applying optimal control theory to maximize annuiti production in a grazing system with a seasonal growth rate function. It sketches out a simple model for predicting the effects of stocking density on pasture quality through time and discusses possible approaches to modelling selective grazing by animals.
