The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 17, Number 5-6 (2007), 1777-1807.
Survival and complete convergence for a spatial branching system with local regulation
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.
Ann. Appl. Probab., Volume 17, Number 5-6 (2007), 1777-1807.
First available in Project Euclid: 3 October 2007
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Birkner, Matthias; Depperschmidt, Andrej. Survival and complete convergence for a spatial branching system with local regulation. Ann. Appl. Probab. 17 (2007), no. 5-6, 1777--1807. doi:10.1214/105051607000000221. https://projecteuclid.org/euclid.aoap/1191419183