KPP Dynamics in Predator–Prey Models: A Survey and a Mussel–Algae Case Study

We discuss traveling fronts in several coupled reaction–diffusion systems that model predator–prey interactions, as well as other systems that share similar structural features. We review some cases where the traveling fronts exist and are small perturbations of fronts in certain scalar equations of Fisher–KPP or Burgers–FKPP type. As a new result consistent with the reviewed cases, we establish the existence of a previously unobserved family of traveling fronts in a mussel–algae interaction model, in a parameter regime complementary to those studied earlier. These fronts are constructed as perturbations of fronts of a Fisher–KPP‐type scalar equation using geometric singular perturbation theory.