Encyclopedia of Systems Biology

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

Dynamical Systems Theory, Delay Differential Equations

  • Patrick NelsonEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-9863-7_272



Delay differential equations (DDE) are equations whose solution depends on not just a single initial condition at time, t = t 0, but also on the past history of the system. DDEs can be classified as retarded or neutral and continuous or discrete. In general, a discrete delay differential equation can be written as
$$\eqalign{ \frac{{{d^n}y}}{{d{t^n}}} =\ f( {t,\;{a_0}{{(t)}}y(t),\;a_1{{(t)}}y'(t), \ldots a{{(t)}_{{n - 1}}}{y^{{n - 1}}}(t),} \cr {b_0{{(t)}}y(t - \tau ) \ldots b_{{n - 1}}}{{(t)}{y^{{n - 1}}}(t - \tau )}) }$$
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Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  1. 1.CCMB 2017 Palmer CommonsUniversity of MichiganAnn ArborUSA