Initial Conditions for Models of Dynamical Systems

Details Initial Conditions for Models of Dynamical Systems Initial Conditions for Models of Dynamical Systems

1994-11-25

arxiv.org/abs/chao-dyn/9411021v1

Nonlinear Sciences

Chaotic Dynamics

24 pages in standard LaTeX, 66K, no figures

Scientific paper

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

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