Skip to main content

differential equations - Putting NDSolve into ParametricPlot


I am having issues using Manipulate to plot the (numeric) solution to an ODE for different parameter values.


I have a code that has several stages, which seem to all work when I do them one after another. This code solves a system of ODEs (for particular parameter values), then does a parametric plot of the solution. The problem is I need to put the lines together to wrap them around with Manipulate (for I can do this code again easily for different parameter values), and this is causing me a lot of pain.


My initial code is:


(*this is my ODE*)

unforced[x0_, p0_, α_:α, δ_:δ] :=

{x'[t] == p[t],
p'[t] == -α x[t] - δ p[t] + α (x[t])^3,
x[0] == x0,
p[0] == p0
}

(*Choose some parameter values*)

α = -1, δ = 1


(*Solve my ODE*)

s = NDSolve[unforced[x0 = 1, p0 = 1], {x, p}, {t, 20}]

(*Plot It*)

ParametricPlot[Evaluate[{x[t], p[t]} /. s], {t, 0, 20}]

But now I want to be able to Manipulate the parameter values α and δ. So I start putting the lines of code together... and problems happen.


ParametricPlot[Evaluate[{x[t], p[t]}/.

NDSolve[{x'[t] == p[t],
p'[t] == -α x[t] - δ p[t] + α (x[t])^3,
x[0] == 1, p[0] == 0}, {x, p}, {t, 20}]], {t, 0, 20}]

This plots an empty graph. This confuses me because it seems like all I did was substitute into my previous code. Because this doesn't work, I can't put a Manipulate around this. If it worked then I would have tried:


Manipulate[ParametricPlot[Evaluate[{x[t], p[t]} /.
NDSolve[{x'[t] == p[t],
p'[t] == -α x[t] - δ p[t] + α (x[t])^3,
x[0] == 1, p[0] == 0}, {x, p}, {t, 20}]], {t, 0, 20}],
{{α, -1, "α"}, -2, 0}, {{δ, 0, "δ"}, 0, 2}]


How do I get around this problem?




Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

functions - What best practices or performance considerations are there for choosing between Cases, Position, Pick and Select?

Cases , Select , Pick and Position each have different syntaxes and purposes, but there are times when you can express the same calculation equivalently using either of them. So with this input: test = RandomInteger[{-25, 25}, {20, 2}] {{-15, 13}, {-8, 16}, {-8, -19}, {7, 6}, {-21, 9}, {-3, -25}, {21, -18}, {4, 4}, {2, -2}, {-24, 8}, {-17, -8}, {4, -18}, {22, -24}, {-4, -3}, {21, 0}, {19, 18}, {-23, -8}, {23, -25}, {14, -2}, {-1, -13}} You can get the following equivalent results: Cases[test, {_, _?Positive}] {{-15, 13}, {-8, 16}, {7, 6}, {-21, 9}, {4, 4}, {-24, 8}, {19, 18}} Select[test, #[[2]] > 0 &] {{-15, 13}, {-8, 16}, {7, 6}, {-21, 9}, {4, 4}, {-24, 8}, {19, 18}} Pick[test, Sign[test[[All, 2]] ], 1] {{-15, 13}, {-8, 16}, {7, 6}, {-21, 9}, {4, 4}, {-24, 8}, {19, 18}} test[[Flatten@Position[test[[All, 2]], _?Positive] ]] {{-15, 13}, {-8, 16}, {7, 6}, {-21, 9}, {4, 4}, {-24, 8}, {19, 18}} Are there performance or other considerations that should guide which you shou...