Math 6410 • ODE

Consider the bathtub model for the concentrations \(x(t)\ge0\) and \(y(t)\ge0\)
\[
  \begin{aligned}
    \dot{x}&=-9x+y+9x^2y\\
    \dot{y}&=6-y-9x^2y.
  \end{aligned}
\]
\begin{enumerate}
\item[(a)] Give as complete a proof as you can that there exists a nonconstant
periodic orbit.
\item[(b)] State the Hartman-Grobman Theorem. What role does it play in your proof
of (a)?
\end{enumerate}