# Plotting

## Standard plots using the plot recipe from Plots.jl

Plotting is provided by calling recipes to `Plots.jl`

. It means that to plot a branch `br`

, you just need to call

```
#]add Plots # You need to install Plots.jl before your first time using it!
using Plots
plot(br)
```

where `br`

is a branch computed after a call to `br = continuation(...)`

. Plots can be customized using all the keyword arguments provided by Plots.jl. For example, we can change the plotting backend to the GR package and put a title on the plot by doing:

```
gr()
plot!(br, title = "I have a branch!")
```

or you can use a scatter plot

`scatter(br)`

Then to save the plot, use `savefig`

, for example:

`savefig("myplot.png")`

## Specific plotting keyword arguments

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 several branches `br1, br2`

, you can plot them in the same figure by doing

`plot(br1, br2)`

in place of

```
plot(br1)
plot!(br2)
```

The bifurcation points for which the bisection was successful are indicated with circles and with squares otherwise.

Note that the plot recipes use the parameter axis as `xlabel`

, and the passed variable as `ylabel`

.

## 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`record_from_solution`

(see`continuation`

) returns a`Number`

.`x1, x2,...`

if`record_from_solution`

returns a`Tuple`

.- the keys of the
`NamedTuple`

returned by`record_from_solution`

.

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

.

## 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.

## Plotting without the plot recipe

What if you don't want to use Plots.jl? You can define your own plotting functions using the internal fields of `br`

which is of type `ContResult`

. For example, in PyPlot, Gadfly, GR, etc., you can do the following to plot the branch (like the plot recipe `plot(br, vars = (:param, :x))`

):

`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`

. For example, you can change the color depending on the stability:

```
col = [stb ? :green : :red for stb in br.stable]
plot(br.param, br.x, color=col)
```

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))
```

## Standard plots using the Makie.jl [Experimental]

Plotting is also provided by calling recipes to `Makie.jl`

. It means that to plot a branch `br`

, you just need to call

```
#]add GLMakie # You need to install GLMakie.jl before your first time using it!
using GLMakie
BifurcationKit.plot(br)
```

The keyword arguments to `BifurcationKit.plot`

are the same as decribed above in the page. You can also combine diagrams with `BifurcationKit.plot(br1, br2)`

or use `BifurcationKit.plot!(ax, br)`

to add a branch to an existing plot.

### Example

```
using Revise, GLMakie, BifurcationKit
Makie.inline!(true)
q = 1/0
k = 2
F(x, p) = (@. p + x - x^(k+1)/(k+1))
prob = BifurcationProblem(F, [0.8], 1., (@lens _); record_from_solution = (x,p; k...) -> x[1])
opts = ContinuationPar(dsmax = 0.1, dsmin = 1e-3, ds = -0.001, p_min = -1., p_max = 1.)
br = continuation(prob, PALC(), opts)
BifurcationKit.plot(br)
```