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\title{Nonlinear Dynamics Lab}
\author{May 10, 2013}
\date{Report due May 17, 2013}
\maketitle

The work on this task-sheet should be written up in a very brief
(about one type-written page) report.  The equation numbers refer to
equations in the paper C.R. Gray, \emph{An analysis of the
Belousov--Zhabotinskii reaction}, Rose--Hulman Undergraduate
Mathematics Journal \textbf{3}(1), 2002.

You should assume the parameter values stated in the paper, in
particular, $f=3/2$. 

\begin{enumerate}

\item Consider the reduced FKN mechanism for the BZ reaction, given as
equation (8--9) in the paper by Gray.  Get an analytic approximation
for the period of the oscillation using the ``relaxation oscillation''
analysis presented in class.  

(You may use any kind of analytical or numerical integration scheme
when convenient.)

\item \emph{Alternative task:} Solve the Oregonator system (5--7)
numerically and measure the period of oscillation.  

\item Very briefly compare the results from 1 and 2, where you should
refer to the complementary result from one of your classmates.

\item Write a brief description of the laboratory experiment,
listing the chemicals used, their concentrations, and the procedure.
Measure the period of oscillations in the stirred case and describe
the patterns in the unstirred case.

\end{enumerate}

\emph{Note:} In the lab, we will see a Ferroin-catalyzed version of
the BZ reaction, different from the FKN mechanism described in Gray,
where the main reaction pathways include
\begin{gather}
\ce{2 Br^- + Br O_3^- + 3 H^+ + 3 H_2 Mal -> 3 H Br Mal + 3 H_2 O} \\
\ce{BrO_3^- + 4 Ferroin^{2+} + H_2 Mal + 5 H^+ 
    -> 4 Ferriin^{3+} + H Br Mal + 3 H_2O} \\
\ce{4 Ferriin^{3+} + H Br Mal + 2 H_2O -> 4 Ferroin^{2+} + HCOOH + 
    2 CO_2 + 5 H^+ + Br^-}
\end{gather}
However, these reactions are insufficient to explain oscillatory
behavior.  Extending the reaction set to fully describe the observed
dynamics is a nontrivial task, but could be a very rewarding Guided
Research/Thesis project for anyone interested in the mathematical
aspects of chemistry.

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