We 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 neighboring 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 nontrivial equilibrium and complete convergence, as well as long-term coexistence in a related two-type model. Along the way we classify the equilibria and their domain of attraction for the corresponding deterministic coupled map lattice on ℤd.
@article{1191419183,
author = {Birkner, Matthias and Depperschmidt, Andrej},
title = {Survival and complete convergence for a spatial branching system with local regulation},
journal = {Ann. Appl. Probab.},
volume = {17},
number = {1},
year = {2007},
pages = { 1777-1807},
language = {en},
url = {http://dml.mathdoc.fr/item/1191419183}
}
Birkner, Matthias; Depperschmidt, Andrej. Survival and complete convergence for a spatial branching system with local regulation. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp. 1777-1807. http://gdmltest.u-ga.fr/item/1191419183/