Plotting nonlinear ODEs in Julia

General Usage
1

Hey folks. I am writing some instructional materials in a set of Pluto notebooks. The topic is nonlinear ODEs, so there are some plots from the Strogatz textbook that I want to emulate. I was wondering if anyone can tell me the easiest way to replicate these plots in either Plots.jl, or in Makie.jl.

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Writing the plot of the function is easy enough. The tricky point is adding the arrow on the axes, as well as the half-open half-closed circles at the semi-stable fixed points. I know Plots.jl better than I know Makie, but I have not figured out a good way to do this in Plots.jl.

Any help would be appreciated.

Just as some starter code, I could plot the function on the right of the image above. Like I said, it is the arrays and equilibrium points that are throwing me off.

x = LinRange(-2.0, 2.0, 100)
f(x) = x^2
p = Plots.plot(x, f.(x), label="function", xlabel=L"x", ylabel=L"\dot{x}", ylims=(-4, 4))
Plots.scatter!(p, [0], [0], label="equilibria")

Here is the corresponding plot.

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2

One way would be to use annotations:

x = LinRange(-2.0, 2.0, 100)
f(x) = x^2
p = Plots.plot(x, f.(x), label="function", xlabel=L"x", ylabel=L"\dot{x}", ylims=(-4, 4))
Plots.annotate!(p, 0, 0, "◐") # thats \cirfl
Plots.annotate!(p, -1, 0, "▶") # thats \blacktriangleright
Plots.annotate!(p, 1, 0, "▶", framestyle=:origin)
3 Likes
3

Oh yes, this is excellent. Thanks for showing me how to add these additional marks to the plot. This is exactly what I was looking for.