Codice  QDD 58 
Titolo  A selfregulating and patch subdivided population 
Data  20091119 
Autore/i  Belhadji, L.; Bertacchi, D.; Zucca, F. 
Link  Download full text 
Abstract  We consider an interacting particle system on a graph which, from a macroscopic point of view,
looks like ${ mathbb Z}^d$ and, at a microscopic level, is a complete graph of degree $N$ (called a patch).
There are two birth rates: an interpatch one $ lambda$ and an intrapatch one $ phi$. Once a
site is occupied, there is no breeding from outside the patch and the probability $c(i)$ of success of an intrapatch breeding decreases with the size $i$ of the population in the site. We prove the existence of a critical value $ lambda_{cr}( phi, c, N)$ and a critical value $ phi_{cr}( lambda, c, N)$.
We consider a sequence of processes generated by the families of control functions $ {c_i }_{i in N}$ and degrees $ {N_i }_{i in { mathbb N}}$; we prove, under mild assumptions, the existence of a critical value $i_{cr}( lambda, phi,c)$. Roughly speaking we show that, in the limit, these processes behave as the branching random walk on ${ mathbb Z}^d$ with intraneighbor birth rate $ lambda$ and onsite birth rate $ phi$.
Some examples of models that can be seen as particular cases are given. 
