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arXiv · 1205.6394

Stochastic evolution of four species in cyclic competition

C. H. Durney·S. O. Case·M. Pleimling·R. K. P. Zia
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Abstract

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.

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C. H. Durney, S. O. Case, M. Pleimling, R. K. P. Zia. 2012-05-29. Stochastic evolution of four species in cyclic competition. https://doi.org/10.1088/1742-5468%2F2012%2F06%2Fp06014

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