Dear Matt,
I am not sure what exactly you are looking for but here's an example of a so-called SIR system that models the spreading of a disease in a population. Three interrelated variables (susceptibles, infected, recovered) are iterated.
(*equations*)
sus[i_] := sus[i] = sus[i - 1] - \[Rho] sus[i - 1] inf[i - 1];
inf[i_] := inf[i] = inf[i - 1] + \[Rho] sus[i - 1] inf[i - 1] - \[Lambda] inf[i - 1];
rec[i_] := rec[i] = rec[i - 1] + \[Lambda] inf[i - 1];
(*initial conditions and parameters*)
sus[1] = 0.95; inf[1] = 0.05; rec[1] = 0; \[Rho] = 0.2; \[Lambda] = 0.1;
(*time course*)
tcourse = Table[{sus[i], inf[i], rec[i]}, {i, 1, 100}] // AbsoluteTiming
(*Plot*)
ListPlot[Transpose[tcourse]]
Of course there are other ways such as this one (not that easy to read):
(*Parameters*)
c = 0.1; b = 0.2;
Manipulate[results = {{0.05, 0.95, 0.0}};
(*Iterations*)
For[i = 0, i <= 100, i++,
AppendTo[results, {(1 - c) results[[-1, 1]] + b*results[[-1, 1]] results[[-1, 2]], results[[-1, 2]]*(1 - b results[[-1, 1]]), results[[-1, 3]] + c results[[-1, 1]] }]];
(*Plotting*)
ListPlot[Transpose[results]],
{{c, 0.1}, 0.0, 0.9}, {{b, 0.2}, 0.0, 0.9}]
Note that in the second code the "variables" are in a different order. I hope this helps a bit.
M.
