Stability, persistence and structural stability in a classical predator-prey model

A set of Rosenzweig-MacArthur type predator-prey equations are considered. Four different predator response functions are chosen for use in these equations. The fitting parameter for each response function is chosen so that the four functions are closely matched to each other. Numerical simulations are performed for each response function. These simulations show qualitative differences between response functions in model outcome or stability behaviour for some parameters values. The equations are analysed mathematically to produce parameter space plots which show where qualitative changes in solutions occur. It is concluded that Rosenzweig-MacArthur equations are sensitive to the mathematical form used for the predator response function. This sensitivity may lead to different types of stability behaviour that include stable coexistence of both species, persistent oscillations and predator extinction. Hence it is important to consider the underlying biology (whether the predator has alternative prey for example) and the theoretical basis for the form of a predator response function when choosing the type of response function for any model.