Bifurcation problems
The idea behind BifurcationKit
is to compute bifurcation diagrams in memory limited environments where the device can barely hold the current continuation state. We thus disable by default saving all solutions along the branch and all eigenvectors (see ContinuationPar
to change this behaviour). Still, one needs to save a few solution indicators, like for plotting. This is the reason for the function record_from_solution
(see below).
Generic bifurcation problem
BifurcationProblem
is the basic / generic structure for encoding a bifurcation problem ; it holds the following fields:
- the vector field
- an initial guess
- a set of parameters
- a parameter axis
as well as user defined functions for
- plotting,
plot_solution
- recording (
record_from_solution
) indicators about the solution when this one is too large to be saved at every continuation step.
Example
f(x,p) = @. sin(x * p.a)
u0 = zeros(100_000_000)
params = (a = 1.0, b = 2.0)
# record a few components / indicators about x
myRecord(x,p) = (x1 = x[1], max = maximum(x), nrm = norm(x, Inf))
prob = BifurcationProblem(f, u0, p, (@lens _.a);
record_from_solution = myRecord
)
Problem modification
In case you want to modify an existing problem, you should use the following method
BifurcationKit.re_make
— Methodre_make(
prob;
u0,
params,
lens,
record_from_solution,
plot_solution,
J,
Jᵗ,
d2F,
d3F
)
This function changes the fields of a problem ::AbstractBifurcationProblem
. For example, you can change the initial condition by doing
re_make(prob; u0 = new_u0)
Example
using BifurcationKit, Setfield
F(x,p) = @. p.a + x^2
# parameters
par = (a = 0., b = 2)
prob = BifurcationProblem(F, zeros(3), par, (@lens _.a))
# change u0
prob2 = BifurcationKit.re_make(prob, u0 = rand(3))
┌─ Bifurcation Problem with uType Vector{Float64}
├─ Inplace: false
├─ Symmetric: false
└─ Parameter: a