Abstract
In this paper, we study a diffusive prey–predator model with Beddington–DeAngelis functional response when the intraspecific crowding effect for the prey population disappears in some subdomain $$\Omega _0$$ of their whole habitat. We are concerned about the global dynamics of the system and discuss it based on two coefficients: the growth rate of prey $$\lambda $$ and that of predator $$\mu $$. In particular, the results show that, with the degeneracy of prey population’s intraspecific crowding effect in the subdomain $$\Omega _0$$, the density of prey may tend to infinity in $$\Omega _0$$. On the other hand, the unboundedness of prey means that the solutions of the system lose compactness which may bring difficulty to investigate the long-time behavior of the solutions. Finally, some numerical simulations are presented to support and strengthen our theoretical analysis.
Published Version
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