Piecewise linear models of chemical reaction networks

Details Piecewise linear models of chemical reaction networks Piecewise linear models of chemical reaction networks

2012-01-10

arxiv.org/abs/1201.2072v1

Biology

Quantitative Biology

Molecular Networks

Scientific paper

We show that certain non-linear dynamical systems with non-linearities in the form of Hill functions, can be approximated by piecewise linear dynamical systems. The resulting piecewise systems have closed form solutions that can be used to understand the behavior of the fully nonlinear system. We justify the reduction using geometric singular perturbation theory, and illustrate the results in networks modeling a genetic switch and a genetic oscillator.

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