Interfaces with internal structures in generalized rock-paper-scissors models

Abstract: In this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships, in the context of cyclic predator-prey models with an even number of species $N \ge 8$. We use both stochastic and field theory simulations in one and two spatial dimensions, as well as analytical arguments, to describe the association at the interfaces of mutually neutral individuals belonging to enemy partnerships and to probe their role in the development of the dynamical structures at the interfaces. We identify an interesting behaviour associated to the symmetric or asymmetric evolution of the interface profiles depending on whether $N/2$ is odd or even, respectively. We also show that the macroscopic evolution of the interface network is not very sensitive internal structure of the interfaces. Although this work focus on cyclic predator prey-models with an even number of species, we argue that the results are expected to be quite generic in the context of spatial stochastic May-Leonard models.