In the description of the dynamics of excitons in semiconductor physics, one finds the following problem                 where (0) = 1 and (0) = 1. Also,  and  are constants that satisfy 0  > 0....

In the description of the dynamics of excitons in semiconductor physics, one finds the following problem

where
(0) = 1 and
(0) = 1. Also,
 and
 are constants that satisfy 0
<> > 0. Note,
() and
() are densities and are therefore non-negative.

(a) Taking
 = 0.1 and
 = 0.2, generate synthetic data for
 and
 using 500 equally spaced time points over the interval 0
 ≤ 200.

(b) Using either the data from part (a), or a data set provided, find
 and
. Also, plot the data and numerical solution using these parameter values. If you modify the minimization code make sure to explain why you did so, and what exactly you did change.