Encyclopedia of Systems Biology

2013 Edition
| Editors: Werner Dubitzky, Olaf Wolkenhauer, Kwang-Hyun Cho, Hiroki Yokota

Ordinary Differential Equation (ODE)

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-9863-7_1419




An ordinary differential equation is an equality that involves a function and its derivatives with respect to only one independent variable.

Ordinary differential equations (ODEs) are frequently used for modeling biological systems to characterize the dependence of certain properties on time (Klipp et al. 2005). This time behavior can be described by a set of ODEs:
$$ \frac{{d{x_i}}}{{dt}} \;= {f_i} \ \left( {{x_1}, \ldots, {x_n},{p_1}, \ldots, {p_l},t} \right)\quad i = 1, \ldots, n $$
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  1. Klipp E, Herwig R, Kowald A, Wierling C, Lehrach H (2005) Systems biology in practice. Wiley-VCH, WeinheimGoogle Scholar

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© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Maria Rodriguez-Fernandez
    • 1
  • Francis J. DoyleIII
    • 1
  1. 1.Department of Chemical EngineeringInstitute for Collaborative Biotechnologies, University of CaliforniaSanta BarbaraUSA