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

• 成果类型: Article
• 署名作者: Birkner, Matthias; Depperschmidt, Andrei
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051607000000221
• 发表日期: 2007
• 页码: 1777-1807
• 关键词: POPULATION; MODEL; COMPETITION

摘要

We study a discrete time spatial branching system on Z(d) With log iStic- 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).