92C42 Systems biology, networks
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In this paper, a down-to-earth approach to purely data-based modelling
of unknown dynamical systems is presented. Starting from a classical, explicit ODE
formulation y=f(t,y) of a dynamical system, a method determining the unknown
right-hand side f(t,y) from some trajectory data y_k(t_j), possibly very sparse, is given.
As illustrative examples, a semi-standard predator-prey model is reconstructed from a
data set describing the population numbers of hares and lynxes over a period of twenty
years [1], and a simple damped pendulum system with a highly non-linear right-hand
side is recovered from some artificial but very sparse data [2].
Modelling, parameter identification, and simulation play an important rôle in Systems Biology. In recent years, various software packages have been established for scientific use in both licencing types, open source as well as commercial. Many of these codes are based on inefficient and mathematically outdated algorithms. By introducing the package BioPARKIN recently developed at ZIB, we want to improve this situation significantly. The development of the software BioPARKIN involves long standing mathematical ideas that, however, have not yet entered the field of Systems Biology, as well as new ideas and tools that are particularly important for the analysis of the dynamics of biological networks. BioPARKIN originates from the package PARKIN, written by P.Deuflhard and U.Nowak, that has been applied successfully for parameter identification in physical chemistry for many years.