Junctions and spiral patterns in generalized rockpaperscissors models
Abstract
We investigate the population dynamics in generalized rockpaperscissors models with an arbitrary number of species N. We show that spiral patterns with N arms may develop both for odd and even N, in particular in models where a bidirectional predation interaction of equal strength between all species is modified to include one Ncyclic predatorprey rule. While the former case gives rise to an interface network with Ytype junctions obeying the scaling law L∝t^{1/2}, where L is the characteristic length of the network and t is the time, the latter can lead to a population network with Narmed spiral patterns, having a roughly constant characteristic length scale. We explicitly demonstrate the connection between interface junctions and spiral patterns in these models and compute the corresponding scaling laws. This work significantly extends the results of previous studies of population dynamics and could have profound implications for the understanding of biological complexity in systems with a large number of species.
 Publication:

Physical Review E
 Pub Date:
 September 2012
 DOI:
 10.1103/PhysRevE.86.036112
 arXiv:
 arXiv:1205.6078
 Bibcode:
 2012PhRvE..86c6112A
 Keywords:

 89.75.Fb;
 87.18.h;
 87.10.e;
 Structures and organization in complex systems;
 Multicellular phenomena;
 General theory and mathematical aspects;
 Physics  Biological Physics;
 Quantitative Biology  Populations and Evolution
 EPrint:
 6 pages, 8 figures, published version