The Annals of Applied Probability

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

Matthias Birkner and Andrej Depperschmidt

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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 information

Ann. Appl. Probab., Volume 17, Number 5-6 (2007), 1777-1807.

First available in Project Euclid: 3 October 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 92D40: Ecology

Regulated population survival coexistence complete convergence


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.

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