# ListPlot of recurrence equation of multiple variables [closed]

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?

-

## closed as too localized by Mr.Wizard♦Feb 27 '13 at 4:23

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## 1 Answer

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.

-
Thanks Mark; I overlooked that part. (Always remember you can vote to reopen if you wish.) –  Mr.Wizard Feb 27 '13 at 4:38
Wow, Mark, that's fantastic! Thank you for teaching me about MapIndexed. Programming inside a function call is always a challenge. –  user6120 Feb 27 '13 at 4:44
@Mr.Wizard No biggie - I'll save my reopen votes for the WolframAlpha questions. :) –  Mark McClure Feb 27 '13 at 5:25
@user6120 No problem! I hope your students like it. –  Mark McClure Feb 27 '13 at 5:25
Showing this tomorrow in a control theory class at MIT. Thanks again! –  user6120 Feb 27 '13 at 5:37