BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Effect of population size in a Prey-Predator model
DTSTART:20130301T101500
DTEND:20130301T110000
DTSTAMP:20260916T061406Z
UID:24cc42f9ed5778cd326c08f4bcb9369a149645d483be1ae3d978427d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Claude Lobry\nEPI Modemic\, Inra-Inria\, 2 place Viala\, Montp
 ellier.\n[Please note that this seminar will be in French]\nIn population 
 dynamics state variables represent the size of some population and\, by th
 e way\, are ``integers".\nBirth and death processes and similar stochastic
  models are suitable models to represent discrete populations.\nNeverthele
 ss it is widely recognized that\, when  populations are large\, thanks to
  the central limit theorem\, ordinary\ndifferential equations with continu
 ous state variables are suitable approximations. But what means ``large " 
 ?\nWe consider a stochastic version of the basic predator-prey differentia
 l equation model of Rosenzweig-MacArthur.\nOur  model contains a paramete
 r ω which can be interpreted as the number of individuals for one unit of
  prey.\nThis means that if x denotes the quantity of prey in the different
 ial equation model\,  x = 1 means that there are ω individuals in the di
 scontinuous model.\nIt is shown by the mean of simulations and explained b
 y a mathematical analysis based on results in singular perturbation theory
  (the so called theory of Canards) that qualitative properties of the mode
 l like persistence or extinction are dramatically sensitive to ω. For ins
 tance\, in our example\, if ω = 10^7  the model predicts extinction and 
 if ω = 10^8 it predicts persistence. This means that we must be very caut
 ious when we use continuous variables in place of jump processes in dynami
 c population modeling even when we use stochastic differential equations i
 n place of a deterministic ones.
LOCATION:ME C2 405
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR