Plotting system of recursive sequences [duplicate]

If I have a system of recursive sequences like

x[n+1]=2x[n]+5(y[n])^2

y[n+1]=.5x[n]-3(y[n])^2

How can I plot it as a curves {x[n],n} and {y[n],n} in the same figure?? When I work with this code, I get the error as in the image ]1

• – zhk
Jan 19 '17 at 5:37
• What initial conditions, {x, y} do you wish? Jan 19 '17 at 5:50
• Thank you very much! "But when I copied this code in Mathematica 7. I get the error message: ListLinePlot::optx: Unknown option PlotLegends in ListLinePlot[{{1.,22.,705.25},{2.,-11.5,-385.75}},<<4>>,PlotLegends->{x,y}]. >>" Jan 19 '17 at 14:25
• @Raafat Load the package. << PlotLegends
– zhk
Jan 19 '17 at 15:23
• @Raafat Mathematica 7 does not have PlotLegends; you will need to load the package as MMM says but also use PlotLegend with no s, and parameters for the two options are not the same. Jan 19 '17 at 23:29

RecurrenceTable will be useful here. Note, I choose random initial conditions.

sol = RecurrenceTable[{x[n + 1] == 2  x[n] + 5 (y[n])^2,
y[n + 1] == 0.5  x[n] - 3 (y[n])^2, x == 1, y == 2}, {x,
y}, {n, 0, 2}, WorkingPrecision -> MachinePrecision];

ListLinePlot[Transpose@sol,
PlotStyle -> {Directive[Red, Thick],
Directive[Blue, AbsoluteDashing[{10, 10}]]}, Joined -> True,
Frame -> True, FrameLabel -> (Style[#, 22, Bold] & /@ {"n", ""}),
PlotLegends -> {x,  y}] You can also use @David G. Stork method.

x[n_] := 2  x[n - 1] + 5 (y[n - 1])^2;
y[n_] := 0.5  x[n - 1] - 3 (y[n - 1])^2;
x := 1;
y := 2;
ListLinePlot[Transpose@Table[{x[n], y[n]}, {n, 0, 2}],
PlotLegends -> {"x", "y"}]
• No, but I have an error when i do! Jan 19 '17 at 14:56
• @Raafat Doing what produces an error?
– zhk
Jan 19 '17 at 14:57
• I have copied the code and use it in mathematica. But it gives the error message: " ListLinePlot::optx: Unknown option PlotLegends in ListLinePlot[{{1,22,705.25},{2,-11.5,-385.75}},PlotLegends->{x,y}]. >>" Jan 19 '17 at 15:01
• Thank you for help! the code does work. But without "PlotLegends -> {"x", "y"}"!! Do you have a solution to that ?! Jan 19 '17 at 15:23
• @Raafat load the package. << PlotLegends`
– zhk
Jan 19 '17 at 15:24