(*^
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                                                    A Neat Problem

The cell below illstrates how the Mathematica procedure  NDSolve  can be used to investigate problems like the problem in this module.  Evaluate it now.
;[s]
7:0,1;66,0;102,2;113,0;125,1;132,0;203,3;221,-1;
4:3,13,9,Times,0,12,0,0,0;2,13,9,Times,1,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect]
Clear[solution, a, b, c]

high := 4

a := 1
b := 1
c := 1

solution = NDSolve[
  {x'[t] == a * (y[t] - x[t]),
   y'[t] == b * (x[t] - y[t]) - c * y[t],
   x[0] == 0,
   y[0] == 6},
  {x, y},
  {t, 0, high}];
   
Plot[{x[t] /. solution, 
      y[t] /. solution},
     {t, 0, high},
     PlotRange -> {0, 6},
     PlotStyle -> {{RGBColor[1, 0, 0]},
                   {RGBColor[0, 0, 1]}}]
:[font = special1; inactive; preserveAspect]

This give us an immediate partial answer to our question. What is it? Notice that we still have lots of questions. The most important question is -- Why? We should also ask whether this always happens or we just happened to pick one particular situation in which it did happen. 
^*)