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

Birkner M, Depperschmidt A (2007)

Publication Type: Journal article, Original article

Publication year: 2007

Journal

Annals of Applied Probability Institute of Mathematical Statistics (IMS)

Book Volume: 17

Pages Range: 1777-1807

Journal Issue: 5-6

DOI: 10.1214/105051607000000221

Abstract

We study a discrete time spatial branching system on 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 ℤ^d. © Institute of Mathematical Statistics, 2007.

Authors with CRIS profile

Andrej Depperschmidt Lehrstuhl für Mathematische Stochastik

Involved external institutions

Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) - Leibniz-Institut im Forschungsverbund Berlin e. V.

Germany (DE)

How to cite

APA:

Birkner, M., & Depperschmidt, A. (2007). Survival and complete convergence for a spatial branching system with local regulation. Annals of Applied Probability, 17(5-6), 1777-1807. https://dx.doi.org/10.1214/105051607000000221

MLA:

Birkner, Matthias, and Andrej Depperschmidt. "Survival and complete convergence for a spatial branching system with local regulation." Annals of Applied Probability 17.5-6 (2007): 1777-1807.

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