We study a cyclic Lotka - Volterra model of N interacting species populating a d -dimensional lattice. In the realm of a Kirkwood approximation, a critical number of species above which the system fixates is determined analytically. We find in dimensions d = 1,2,3, in remarkably good agreement with simulation results in two dimensions.
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Frachebourg et al. (1998) studied this question.
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