Creating a dynamic plot directly from the recurrence relation

Question

I have the following recurrence relation that has no general solution:

$$x(t+1) = \frac{x^2 + x(1-x)(1-sh)}{x^2 + 2x(1-x)(1-sh) + (1-x)^2(1-s)}$$

In Mathematica language it gives:

x[t + 1] == (x[t]^2 + x[t] (1 - x[t]) (1 - s h))/(
   x[t]^2 + 2 x[t] (1 - x[t]) (1 - s h) + (1 - x[t])^2 (1 - s)  )

---

I'd like to plot $x$ as a function of $t$ (range{0,100}). How can I do this?

Also, that would be awesome if I could directly on my plot, modify the values of $h$ and $s$ in the range {0,1}

Answer 1

Maybe try something like

ClearAll@plotter
plotter[s_, h_] := 
 plotter[s, h] = 
  ListPlot[RecurrenceTable[{x[t + 1] == 
      N[(x[t]^2 + x[t] (1 - x[t]) (1 - s h))/(x[t]^2 + 
          2 x[t] (1 - x[t]) (1 - s h) + (1 - x[t])^2 (1 - s))], 
     x[0] == 7}, x, {t, 0, 16}]
   ,
   PlotRange -> {0, 1}
   ]

Manipulate[plotter[s, h], {{s, 1}, 1, 5, 1}, {{h, 2}, 2, 5, 1}]

which gives

Before I applied a transformation to the recurrence table, but there must have been a mistake, because that now seems unnecessary.