ListPlot of recurrence equation of multiple variables [closed]

Question

I'm working on a class demo of recurrence equations and I want to show the impact of different parameter values using Manipulate. Here's my code:

Manipulate[
 ListPlot[
  RecurrenceTable[
   {s[n + 1] == 
     s[n] - \[Gamma]*(i[n]/PP) s[n] + \[Beta] (PP - s[n]) - \[Beta] PP x,
    i[n + 1] == i[n] + \[Gamma] (i[n]/PP) s[n] - \[Rho]*i[n] - \[Beta]*i[n],
    s[1] == 8000,
    i[1] == 2000
    },
   {s, i},
   {n, 1, 10},
   ],
  PlotRange -> All,
  Joined -> True
  ],
 {\[Gamma], 0.1, 0.5},
 {\[Beta], 0.01, 0.5},
 {\[Rho], 0.1, 0.5},
 {PP, 10000, 20000},
 {x, 0, 1}
 ]

This code shows the phase space plot of s vs. i. How do I produce a plot of the two series s and i as dependent variables of, say,n?

Bonus question: how do I fix the PlotRange of the ListPlot so that it can fit even the largest curve in phase space?

Answer 1

First, you have an extra comma in {n, 1, 10}, that you must remove.

Second, simply set an explicit range with e.g. PlotRange -> {{-3000, 12000}, {0, 3000}}.
I did not try to determine the maximum extent; I leave that as an exercise for you.

And, finally, the following code will plot both parts as functions of n:

Manipulate[
 values = RecurrenceTable[
   {s[n + 1] == 
     s[n] - \[Gamma]*(i[n]/PP) s[n] + \[Beta] (PP - s[n]) - \[Beta] PP x,
    i[n + 1] == i[n] + \[Gamma] (i[n]/PP) s[n] - \[Rho]*i[n] - \[Beta]*i[n],
    s[1] == 8000,
    i[1] == 2000
    },
   {s, i},
   {n, 1, 10}
   ];
 ListPlot[
  MapIndexed[{#2[[2]],#}&,Transpose[values],{2}],
  PlotRange -> All,
  Joined -> True
  ],
 {\[Gamma], 0.1, 0.5},
 {\[Beta], 0.01, 0.5},
 {\[Rho], 0.1, 0.5},
 {PP, 10000, 20000},
 {x, 0, 1}
]

You can grab just the MapIndexed[{#2[[2]],#}&,Transpose[values],{2}], if you care to try to figure that out.