Survival and complete convergence for a spatial branching system with local regulation

Details Survival and complete convergence for a spatial branching system with local regulation Survival and complete convergence for a spatial branching system with local regulation

2007-11-05

arxiv.org/abs/0711.0649v1

Annals of Applied Probability 2007, Vol. 17, No. 5-6, 1777-1807

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/105051607000000221 the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051607000000221

We study a discrete time spatial branching system on $\mathbb{Z}^d$ 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 $\mathbb{Z}^d$.

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