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- ItemSurvival and complete convergence for a spatial branching system with local regulation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Birkner, Matthias; Depperschmidt, AndrejWe study a discrete time spatial branching system on Zd with logistic-type local regulation at each deme depending on a weighted average of the population in neighbouring demes. We show that the system survives for all time with positive probability if the competition term is small enough. For a restricted set of parameter values, we also obtain uniqueness of the non-trivial equilibrium and complete convergence, as well as long-term coexistence in a related two-type model.