Initial Conditions for Models of Dynamical Systems
  The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with appropriate initial conditions, so that it faithfully reproduces the long-term behaviour of the original high-dimensional dynamical system. Our method involves putting the dynamical system into normal form, which not only generates the low-dimensional model, but also provides the correct initial conditions for the model. We illustrate the method with several examples.   Keywords: normal form, isochrons, initialisation, centre manifold 
Stephen M. Cox (University of Nottingham), A. J. Roberts (University   of Southern Queensland)