David Lipshutz (Brown University)
Title: Periodic Oscillations in a Genetic Circuit with Delayed Negative Feedback
Dynamical system models with delayed feedback, state constraints and small noise arise in a variety of applications in biology. Under certain conditions oscillatory behavior has been observed. Here we consider a prototypical fluid model approximation for such a system --- a one-dimensional delay differential equation with reflection. We provide sufficient conditions for the existence, stability and uniqueness of slowly oscillating periodic solutions of such equations. We illustrate our findings with a simple genetic circuit model. This is joint work with Ruth Williams.