## Dynamical Systems Seminar

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.