2 research outputs found
Stochastic evolution of four species in cyclic competition
We study the stochastic evolution of four species in cyclic competition in a
well mixed environment. In systems composed of a finite number 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 , 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 , 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. Mec
Cyclic competition of four species: domains and interfaces
We study numerically domain growth and interface fluctuations in one- and
two-dimensional lattice systems composed of four species that interact in a
cyclic way. Particle mobility is implemented through exchanges of particles
located on neighboring lattice sites. For the chain we find that domain growth
strongly depends on the mobility, with a higher mobility yielding a larger
domain growth exponent. In two space dimensions, when also exchanges between
mutually neutral particles are possible, both domain growth and interface
fluctuations display universal regimes that are independent of the predation
and exchange rates.Comment: 14 pages, 7 figures, version accepted for publication in J. Stat.
Mec