A predator-prey diffusion model in age-dependent population dynamics
An age-structured predator-prey model in which the predation rate is a function of prey age and in which both predator and prey are allowed to diffuse in a one-dimensional habitat is considered. The prey dynamics are governed by the McKendrick-von Foerster equation with an added Laplacian to account for diffusion. The predator's dynamics are taken to be age independent. The functional response is of Holling II type. The prey birth rate is assumed linear. Zero flux conditions are imposed on the ends of the finite habitat interval. The author proves two results. First, if the prey's inherent net reproductive rate N is less than one then both predator and prey populations tend to zero. Secondly, if \(N>1\) then there exists a unique stationary solution in which the predator is absent. This stationary solution is stable if the growth rate of the predator S (at this stationary solution) is negative and is unstable if \(S>0\). Unfortunately the author does not address the possibility of coexistence. For example, a branch of coexistence states presumably bifurcates from this stationary solution at \(S=0\).
scientific article; zbMATH DE number 4154277