Qualitative analysis of a diffusive prey–predator model

In this work we examine a Lotka–Volterra model with diffusion describing the dynamics of multiple interacting prey and predator species. We show that the solution exists, and is unique, bounded, nonnegative, and globally defined. We also prove the non-existence of nonconstant steady state solutions if certain conditions are satisfied. For the particular case of two prey (e.g., engineered and native, respectively) and one common predator species, by performing a linear stability analysis about the initial native-dominant steady state, we determine under which conditions the engineered species invasion succeeds.