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

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.

5 pages, 6 figures, published version

References in corpus (6)

• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Exact results for curvature-driven coarsening in two dimensions
• Self-organizing patterns maintained by competing associations in a six-species predator-prey model
• Segregation process and phase transition in cyclic predator-prey models with even number of species
• Dynamics of domain wall networks with junctions
• General Properties of a System of $S$ Species Competing Pairwise

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