This paper is devoted to investigating the pattern dynamics of Lotka–Volterra cooperative system with nonlocal effect and finding some new phenomena. Firstly, by discussing the Turing bifurcation, we build the conditions of Turing instability, which indicates the emergence of Turing patterns in this system. Then, by using multiple scale analysis, we obtain the amplitude equations about different Turing patterns. Furthermore, all possible pattern structures of the model are obtained through some transformation and stability analysis. Finally, two new patterns of the system are given by numerical simulation.

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.