Mathematical models of animal grazing systems

The behaviour of simple predator-prey systems is well-known and was exploited to enable some general conclusions to be made about the stability of and productivity in extensive herbivore-plant grazing systems. The techniques employed were mainly graphical and, hence, lacked the mathematical bite for a full analytical discussion of the influencing parameters to be made. This paper attempts to remedy this deficiency. Then it turns to the more difficult problem when spatio-temporal variations are considered. The first part provides an opportunity to illustrate the occurrence of Hopf bifurcation and the appearance of oscillatory modes, the second part allows some interesting wave phenomena to be studied. 6 refs, 2 figs