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                           Discrete and Continuous Dynamical Systems

The cell below defines the discrete dynamical system used as an example in the browser window.  Evaluate it now.
;[s]
4:0,1;68,0;166,2;181,0;183,-1;
3:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Supply[p_] := 1000 p - 400
Demand[p_] := 1000 - 500 p

p[1] := 0.50
p[n_] := p[n] =
         p[n - 1] + k (Demand[p[n-1]] - Supply[p[n-1]])

k := 0.0002
:[font = special1; inactive; preserveAspect; ]
The next cell prints and plots the first twenty years of this model.  Evaluate it now.
;[s]
3:0,0;69,1;85,0;87,-1;
2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
TableForm[Table[{i, p[i]}, {i, 1, 20}]]
ListPlot[Table[{i, p[i]}, {i, 1, 20}],
         PlotJoined -> True,
         PlotRange -> {0, 2}]
:[font = special1; inactive; preserveAspect; ]
You can answer the questions about the discrete dynamical systems by changing the intitial condition, p[1], and the value of k.

The next cell computes numerical estimates for the initial value problem used as an example in the browser window.  Evaluate it now.
;[s]
7:0,0;102,1;106,0;125,1;126,0;245,2;260,0;262,-1;
3:4,13,9,Times,0,12,0,0,0;2,13,9,Times,1,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[solution, p, k]

InitialCondition := 0.50
k := 0.0002

solution=NDSolve[
  {p'[t] == k (Demand[p[t]] - Supply[p[t]]),
   p[0] == InitialCondition}, 
   {p}, {t, 0, 20}];
   
Plot[p[t] /. solution, {t, 0, 20},
     PlotRange -> {0, 2}]
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You can answer the questions about continuous dynamical systems by changing the values of InitialCondition and k.
;[s]
5:0,0;90,1;106,0;111,1;112,0;114,-1;
2:3,13,9,Times,0,12,0,0,0;2,13,9,Times,1,12,0,0,0;
^*)