WIAS Preprint No. 1147, (2006)

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



Authors

  • Birkner, Matthias
  • Depperschmidt, Andrej

2010 Mathematics Subject Classification

  • 60K35 92D40

Keywords

  • Regulated population, survival, coexistence, complete convergence

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 neighbouring 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 non-trivial equilibrium and complete convergence, as well as long-term coexistence in a related two-type model.

Appeared in

  • Ann. Probab., 17 (2007) pp. 1777-1807.

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