A spatially heterogeneous predator-prey model

Abstract

This paper introduces a spatially heterogeneous diffusive predator–prey model unifying the classical Lotka–Volterra and Holling–Tanner ones through a prey saturation coefficient, \begin{document}$ m(x) $\end{document} , which is spatially heterogenous and it is allowed to 'degenerate'. Thus, in some patches of the territory the species can interact according to a Lotka–Volterra kinetics, while in others the prey saturation effects play a significant role on the dynamics of the species. As we are working under general mixed boundary conditions of non-classical type, we must invoke to some very recent technical devices to get some of the main results of this paper.