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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Abstract

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

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

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1191419183

Digital Object Identifier
doi:10.1214/105051607000000221

Mathematical Reviews number (MathSciNet)
MR2358641

Zentralblatt MATH identifier
1139.60047

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

Keywords
Regulated population survival coexistence complete convergence

Citation

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


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