matplotlib Code

\section{Lotka-Volterra Equations}
\label{sec:lotka_volterra}

\lstinputlisting[label=code:lotka_volterra,caption={IGNORED}]{problems/lotka_volterra.py}

\begin{figure}
\begin{centering}\includegraphics[width=4in]{fig/lotka_volterra}\par\end{centering}

\caption{\label{fig:lotka_volterra}Upper panel shows population
  trajectories for rabbits (blue) and foxes (green) simulated using
  the Lotka-Volterra population dynamics equations.  Lower panel shows
  the phase-plane trajectories, direction field and nullclines.}
\end{figure}