STABILITY, PERSISTENCE AND STRUCTURAL STABILITY IN A CLASSICAL PREDATOR-PREY MODEL

A set of Rosenzweig-MacArthur type predator-prey equations are conside red. Four different predator response functions are chosen for use in these equations. The fitting parameter for each response function is c hosen so that the four functions are closely matched to each other. Nu merical simulations are performed for each response function. These si mulations show qualitative differences between response functions in m odel outcome or stability behaviour for some parameters values. The eq uations are analysed mathematically to produce parameter space plots w hich show where qualitative changes in solutions occur. It is conclude d that Rosenzweig-MacArthur equations are sensitive to the mathematica l form used for the predator response function. This sensitivity may l ead to different types of stability behaviour that include stable coex istence of both species, persistent oscillations and predator extincti on. Hence it is important to consider the underlying biology (whether the predator has alternative prey for example) and the theoretical bas is for the form of a predator response function when choosing the type of response function for any model.