Von-Neumann's and related scaling laws in Rock-Paper-Scissors type models

TL;DR

This paper explores a family of symmetric Rock-Paper-Scissors models, revealing complex phase structures, domain formation, and interface dynamics that resemble phenomena in condensed matter and cosmology, with potential biological implications.

Contribution

It introduces a new class of $Z_N$ symmetric models with diverse phases and analyzes their interface-driven pattern formation and evolution.

Findings

Multiple distinct phases identified in the models

Formation of domain structures with curvature-driven interfaces

Pattern formation analogous to nonlinear systems in physics

Abstract

We introduce a family of Rock-Paper-Scissors type models with $Z_N$ symmetry ($N$ is the number of species) and we show that it has a very rich structure with many completely different phases. We study realizations which lead to the formation of domains, where individuals of one or more species coexist, separated by interfaces whose (average) dynamics is curvature driven. This type of behavior, which might be relevant for the development of biological complexity, leads to an interface network evolution and pattern formation similar to the ones of several other nonlinear systems in condensed matter and cosmology.