We present a stochastic approach to modeling the dynamics of coexistence ofprey and predator populations. It is assumed that the space of coexistence isexplicitly subdivided in a grid of cells. Each cell can be occupied by only oneindividual of each species or can be empty. The system evolves in timeaccording to a probabilistic cellular automaton composed by a set of localrules which describe interactions between species individuals and mimic theprocess of birth, death and predation. By performing computational simulations,we found that, depending on the values of the parameters of the model, thefollowing states can be reached: a prey absorbing state and active states oftwo types. In one of them both species coexist in a stationary regime withpopulation densities constant in time. The other kind of active state ischaracterized by local coupled time oscillations of prey and predatorpopulations. We focus on the self-organized structures arising fromspatio-temporal dynamics of the coexistence. We identify distinct spatialpatterns of prey and predators and verify that they are intimally connected tothe time coexistence behavior of the species. The occurrence of a preypercolating cluster on the spatial patterns of the active states is alsoexamined.
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