This paper introduces a spatially heterogeneous diffusive predator–prey model unifying the classical Lotka–Volterra and Holling–Tanner ones through a prey saturation coefficient, $ m(x) $, 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.
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Figure 5. The coexistence wedges of Figure 4 when $ \mathrm{Int\, }m^{-1}(0)\neq \emptyset $
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Stability of the semitrivial solutions
Stability of
An admissible component
By Theorem 5.1, (5) admits a coexistence state for each
The coexistence wedges of Figure 4 when