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Abstract: We analyze a probabilistic cellular automaton describing the dynamics ofcoexistence of a predator-prey system. The individuals of each species arelocalized over the sites of a lattice and the local stochastic updating rulesare inspired on the processes of the Lotka-Volterra model. Two levels ofmean-field approximations are set up. The simple approximation is equivalent toan extended patch model, a simple metapopulation model with patches colonizedby prey, patches colonized by predators and empty patches. This approximationis capable of describing the limited available space for species occupancy. Thepair approximation is moreover able to describe two types of coexistence ofprey and predators: one where population densities are constant in time andanother displaying self-sustained time-oscillations of the populationdensities. The oscillations are associated with limit cycles and arise througha Hopf bifurcation. They are stable against changes in the initial conditionsand, in this sense, they differ from the Lotka-Volterra cycles which depend oninitial conditions. In this respect, the present model is biologically morerealistic than the Lotka-Volterra model.



Autor: Tânia Tomé, Kelly C de Carvalho

Fuente: https://arxiv.org/



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