Plotting

Plotting branches

Plotting is provided by calling Plots.jl. It means that to plot a branch br, you just need to call

plot(br)

where br is a branch computed after a call to br, = continuation(...). You can use the keywords provided by Plots.jl and the different backends. You can thus call

scatter(br)
plot!(br, branchlabel = "continuous line")

The available arguments specific to our plotting methods are

• plotfold = true: plot the fold points with black dots
• putspecialptlegend = true: display the legend corresponding to the bifurcation points
• vars = nothing: see below
• plotstability = true: display the stability of the branch
• plotspecialpoints = true: plot the special (bifurcation) points on the branch
• branchlabel = "fold branch": assign label to a branch which is printed in the legend
• linewidthunstable: set the linewidth for the unstable part of the branch
• linewidthstable: set the linewidth for the stable part of the branch
• plotcirclesbif = false use circles to plot bifurcation points
• applytoX = identity apply transformation applytoX to x-axis
• applytoY = identity apply transformation applytoY to y-axis

If you have severals branches br1, br2, you can plot them in the same figure by doing

plot(br1, br2)

in place of

plot(br1)
plot!(br2)

Choosing Variables

You can select which variables to plot using the keyword argument vars, for example:

plot(br, vars = (:param, :x))

The available symbols are :x, :param, :itnewton, :itlinear, :ds, :θ, :n_unstable, :n_imag, :stable, :step,... and:

• x if recordFromSolution (see continuation) returns a Number.
• x1, x2,... if recordFromSolution returns a Tuple.
• the keys of the NamedTuple returned by recordFromSolution.

The available symbols are provided by calling propertynames(br.branch).

Plotting directly using the field names

You can define your own plotting functions using the internal fields of br which is of type ContResult. For example, the previous plot can be done as follows:

plot(br.branch.param, br.branch.x)

You can also have access to the stability of the points by using br.stable. More information concerning the fields can be found in ContResult.

You can also plot the spectrum at a specific continuation step::Int by calling

# get the eigenvalues
eigvals = br.eig[step].eigenvals

# plot them in the complex plane
scatter(real.(eigvals), imag.(eigvals))

Plotting bifurcation diagrams

To do this, you just need to call

plot(diagram)

where diagram is a branch computed after a call to diagram = bifurcationdiagram(...). You can use the keywords provided by Plots.jl and the different backends. You can thus call scatter(diagram). In addition to the options for plotting branches (see above), there are specific arguments available for bifurcation diagrams

• code specify the part of the bifurcation diagram to plot. For example code = (1,1,) plots the part after the first branch of the first branch of the root branch.
• level = (-Inf, Inf) restrict the branching level for plotting.