Stochastic evolution of four species in cyclic competition
| Autor: | Durney, C. H., Case, S. O., Pleimling, M., Zia, R. K. P. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | J. Stat. Mech. (2012) P06014 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-5468/2012/06/P06014 |
| Popis: | We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios, from single species domination to coexistence between non-interacting species. Using exact results and numerical simulations we discuss the temporal evolution of the system for different values of $N$, for different values of the reaction rates, as well as for different initial conditions. As expected, the stochastic evolution is found to closely follow the mean-field result for large $N$, with notable deviations appearing in proximity of extinction events. Different ways of characterizing and predicting extinction events are discussed. Comment: 19 pages, 6 figures, submitted to J. Stat. Mech |
| Databáze: | arXiv |
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