Qualitative analysis of a diffusive prey-predator model with trophic interactions of three levels

Abstract

In this paper, we consider a mathematical model for a prey-predator dynamical system with diffusion and trophic interactions of three levels. In this model, a general trophic function based on the ratio between the prey and a linear function of the predator is used at each level. At the two limits of this trophic function, one recovers the classical prey-dependent and ratio-dependent predation models, respectively. We offer a complete discussion of the dynamical behavior of the model under the homogeneous Neumann boundary condition (the same behavior is also seen in the absence of diffusion). We also discuss existence, uniqueness, stability and bifurcation of equilibrium behavior corresponding to positive steady state solutions under the homogeneous Dirichlet boundary condition. Finally, we give interpretations of some of these results in the context of different predation models.