Long-time behavior of a diffusive prey-predator system with Beddington-DeAngelis functional response in heterogeneous environment

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 Ω₀ 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 λ and that of predator μ. In particular, the results show that, with the degeneracy of prey population's intraspecific crowding effect in the subdomain Ω₀, the density of prey may tend to infinity in Ω₀. 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.