Mathematica Asked on May 1, 2021
I’m working on a project in order to plot a graphical method for finite-difference equations called cobweb method. The next figure was succesful try for
$$x_{t+1} = Rx_t – frac{R}{2000}x_t^2$$
But, when I try with
$$x_{t+1} = cos{x_t},$$
and copy-paste the code I used before, the result was
For some reason Joined->True
doesn’t draw all the lines. Changing a litle bit the number of point plotted, from 17 to 16, the figure is correct
There is a problem, but, where? My code is the following
difEqu[x_] := N[Cos[x]]
traFin = {{0.4,0},{0.4,0.921061},{0.921061,0.921061},{0.921061,0.604976},
{0.604976,0.604976},{0.604976,0.822516},{0.822516,0.822516},{0.822516,0.68038},
{0.68038,0.68038},{0.68038,0.777334},{0.777334,0.777334},{0.777334,0.712786},
{0.712786,0.712786},{0.712786,0.756543},{0.756543,0.756543},{0.756543,0.727213},
{0.727213,0.727213},{0.727213,0.74703},{0.74703,0.74703},{0.74703,0.73371},
{0.73371,0.73371},{0.73371,0.742695},{0.742695,0.742695},{0.742695,0.736649},
{0.736649,0.736649},{0.736649,0.740724},{0.740724,0.740724},{0.740724,0.73798},
{0.73798,0.73798},{0.73798,0.739829},{0.739829,0.739829},{0.739829,0.738584}}
extremos = {{0.4,0},{0.739829,0.738584}}
Show[
Plot[
Evaluate[
{Legended[Style[difEqu[x], RGBColor[0., 0., 1.], Thickness[0.004]],"x[0] = 0.6"],
Legended[Style[x, RGBColor[0., 0., 0.], Thickness[0.004], Dashed],"Identidad"]}
],
{x, 0, 1},
PlotTheme -> "Scientific",
ImageSize -> Large,
PlotRange -> Full,
FrameLabel ->
{Style["x (t)", FontSize -> 35],
Style["x (t+1)", FontSize -> 35]},
LabelStyle -> {FontFamily -> "Arial", 20, RGBColor[0., 0., 0.]}
],
ListPlot[
{traFin, extremos},
PlotStyle -> {{RGBColor[1., 0., 0.],Thickness[0.001]},{RGBColor[1., 0., 0.]}},
Joined -> {True, False}
]
]
I get traFin with another code. The number of iterations here is 16, i.e.
$$x_{16+1} = underbrace{x(x(cdots(}_{text{16 times}}0.4) = 0.738584.$$
Edit: The following code corresponds to 17 iterations:
difEqu[x_] := N[Cos[x]]
traFin = {{0.4,0},{0.4,0.921061},{0.921061,0.921061},{0.921061,0.604976},{0.604976,0.604976},{0.604976,0.822516},{0.822516,0.822516},{0.822516,0.68038},{0.68038,0.68038},{0.68038,0.777334},{0.777334,0.777334},{0.777334,0.712786},{0.712786,0.712786},{0.712786,0.756543},{0.756543,0.756543},{0.756543,0.727213},{0.727213,0.727213},{0.727213,0.74703},{0.74703,0.74703},{0.74703,0.73371},{0.73371,0.73371}, {0.73371,0.742695},{0.742695,0.742695},{0.742695,0.736649}, {0.736649,0.736649},{0.736649,0.740724},{0.740724,0.740724},{0.740724,0.73798},{0.73798,0.73798},{0.73798,0.739829},{0.739829,0.739829},{0.739829,0.738584},{0.738584,0.738584},{0.738584,0.739423}}
extremos = {{0.4,0},{0.739829,0.738584}}
Show[
Plot[
Evaluate[
{Legended[Style[difEqu[x], RGBColor[0., 0., 1.], Thickness[0.004]],"x[0] = 0.6"],
Legended[Style[x, RGBColor[0., 0., 0.], Thickness[0.004], Dashed],"Identidad"]}
],
{x, 0, 1},
PlotTheme -> "Scientific",
ImageSize -> Large,
PlotRange -> Full,
FrameLabel ->
{Style["x (t)", FontSize -> 35],
Style["x (t+1)", FontSize -> 35]},
LabelStyle -> {FontFamily -> "Arial", 20, RGBColor[0., 0., 0.]}
],
ListPlot[
{traFin, extremos},
PlotStyle -> {{RGBColor[1., 0., 0.],Thickness[0.001]},{RGBColor[1., 0., 0.]}},
Joined -> {True, False}
]
]
The problem you are running into is that the ListPlot
is cropping the plot-region in an unlucky way. Put PlotRange->All
as final option into the ListPlot
call and you should be fine.
You could have found this issue yourself by inspecting the plots separately.
Correct answer by halirutan on May 1, 2021
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