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

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

2012-03-29

arxiv.org/abs/1203.6671v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

4 pages, 5 figures

Scientific paper

We introduce a new 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 partnership domains, where two or more species coexist, separated by interfaces whose dynamics is controlled by interactions of identical strength between competing species. We demonstrate that, on average, the velocity of these interfaces, which are relevant for the development of biological complexity, is proportional to their curvature. This behavior leads to pattern formation and interface network evolution which are similar, in a statistical sense, to those of several other nonlinear systems.

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