Spatial dynamics of a nonlocal predator–prey model with double mutation

Abstract

In this paper, we are dedicated to studying the global dynamics of a nonlocal predator–prey model with double mutation. First, by defining a pair of upper and lower solutions, we build a new comparison principle. Furthermore, based on the new comparison principle, we get the existence of the solutions by constructing monotone iterative sequences. Finally, using the quasi-fundamental solution, Gronwall’s inequality and auxiliary functions, the uniqueness and uniform boundedness of the solutions are given. It is worth noting that this paper is the first to introduce the double mutation into the system and obtain the well-posedness and the uniform boundedness of the solutions by more detailed analysis and estimation.