## Dynamical Systems Seminar

Richard RandCornell University
Nonlinear dynamics of a MEMS oscillator
Monday, November 20, 2017 - 3:30pm
Malott 224

Reporting on joint work with Professor A.Zehnder and grad B.Shayak.

“MEMS” stands for “micro-electrico-mechanical system”.

These are very small, very simple “machines”, roughly the size of a red blood cell.
A laser is used to measure the deformation of the MEMS device.
As a side effect, the laser heats the device, resulting in a feedback loop and a vibration via a Hopf bifurcation.
In this seminar a simplified model is considered which involves a second order ODE for the displacement $z$ of the
structure and a first order ODE for the temperature T due to the laser heating:

\begin{align}
z'' + z &= T\\
T' + T &= z^2 - z p,
\end{align}

where $p$ is a parameter around $0.1$.
This system can be shown to support a limit cycle.
In this seminar we consider the nonlinear dynamics of a system of two such coupled oscillators.