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arXiv · 0711.0649

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

Matthias Birkner·Andrej Depperschmidt
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Abstract

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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Matthias Birkner, Andrej Depperschmidt. 2007-11-05. Survival and complete convergence for a spatial branching system with local regulation. https://doi.org/10.1214/105051607000000221

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