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- W2136012912 abstract "We consider an interacting particle system on a graph which, from a macroscopic point of view, looks like ℤ d and, at a microscopic level, is a complete graph of degree N (called a patch). There are two birth rates: an inter-patch birth rate λ and an intra-patch birth rate ϕ. Once a site is occupied, there is no breeding from outside the patch and the probability c ( i ) of success of an intra-patch breeding decreases with the size i of the population in the site. We prove the existence of a critical value λ c (ϕ, c , N ) and a critical value ϕ c (λ, c , N ). We consider a sequence of processes generated by the families of control functions { c n } n ∈ℕ and degrees { N n } n ∈ℕ ; we prove, under mild assumptions, the existence of a critical value n c (λ, ϕ, c ). Roughly speaking, we show that, in the limit, these processes behave as the branching random walk on ℤ d with inter-neighbor birth rate λ and on-site birth rate ϕ. Some examples of models that can be seen as particular cases are given." @default.
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- W2136012912 date "2010-09-01" @default.
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- W2136012912 title "A self-regulating and patch subdivided population" @default.
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- W2136012912 doi "https://doi.org/10.1239/aap/1282924068" @default.
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