Library
Parameters
Missing docstring for BifurcationKit.NewtonPar
. Check Documenter's build log for details.
Missing docstring for BifurcationKit.ContinuationPar
. Check Documenter's build log for details.
Problems
DDEBifurcationKit.ConstantDDEBifProblem
— Typestruct ConstantDDEBifProblem{Tvf, Tdf, Tu, Td, Tp, Tl<:Union{typeof(identity), Nothing, IndexLens, PropertyLens, ComposedFunction}, Tplot, Trec, Tgets, Tδ} <: DDEBifurcationKit.AbstractDDEBifurcationProblem
Structure to hold the bifurcation problem. If don't have parameters, you can pass nothing
.
Fields
VF::Any
: Vector field, typically aBifFunction
. For more information, please look at the website https://bifurcationkit.github.io/DDEBifurcationKit.jl/dev/BifProblemdelays::Any
: function delays. It takes the parameters and return the non-zero delays in anAbstractVector
form. Example:delays = par -> [1.]
u0::Any
: Initial guessdelays0::Any
: initial delays (set internally by the constructor)params::Any
: parameterslens::Union{typeof(identity), Nothing, IndexLens, PropertyLens, ComposedFunction}
: Typically aAccessors.@optic
. It specifies which parameter axis amongparams
is used for continuation. For example, ifpar = (α = 1.0, β = 1)
, we can perform continuation w.r.t.α
by usinglens = (@optic _.α)
. If you have an arraypar = [ 1.0, 2.0]
and want to perform continuation w.r.t. the first variable, you can uselens = (@optic _[1])
. For more information, we refer toAccessors.jl
.plotSolution::Any
: user function to plot solutions during continuation. Signature:plotSolution(x, p; kwargs...)
recordFromSolution::Any
:record_from_solution = (x, p; k...) -> norm(x)
function used record a few indicators about the solution. It could benorm
or(x, p) -> x[1]
. This is also useful when saving several huge vectors is not possible for memory reasons (for example on GPU...). This function can return pretty much everything but you should keep it small. For example, you can do(x, p) -> (x1 = x[1], x2 = x[2], nrm = norm(x))
or simply(x, p) -> (sum(x), 1)
. This will be stored incontres.branch
(see below). Finally, the first component is used to plot in the continuation curve.save_solution::Any
: function to save the full solution on the branch. Some problem are mutable (like periodic orbit functional with adaptive mesh) and this function allows to save the state of the problem along with the solution itself. Signaturesave_solution(x, p)
δ::Any
: delta for Finite differences
Methods
getu0(pb)
callspb.u0
getparams(pb)
callspb.params
getlens(pb)
callspb.lens
setparam(pb, p0)
callsset(pb.params, pb.lens, p0)
record_from_solution(pb)
callspb.record_from_solution
Constructors
ConstantDDEBifProblem(F, delays, u0, params, lens; J, Jᵗ, d2F, d3F, kwargs...)
andkwargs
are the fields above.
DDEBifurcationKit.SDDDEBifProblem
— Typestruct SDDDEBifProblem{Tvf, Tdf, Tu, Td, Tp, Tl<:Union{typeof(identity), Nothing, IndexLens, PropertyLens, ComposedFunction}, Tplot, Trec, Tgets, Tδ} <: DDEBifurcationKit.AbstractDDEBifurcationProblem
Structure to hold the bifurcation problem. If don't have parameters, you can pass nothing
.
Fields
VF::Any
: Vector field, typically aBifFunction
. For more information, please look at the website https://bifurcationkit.github.io/DDEBifurcationKit.jl/dev/BifProblemdelays::Any
: function delays. It takes the parameters and the state and return the non-zero delays in anAsbtractVector
form. Example:delays = (par, u) -> [1. + u[1]^2]
u0::Any
: Initial guessdelays0::Any
: initial delays (set internally by the constructor)params::Any
: parameterslens::Union{typeof(identity), Nothing, IndexLens, PropertyLens, ComposedFunction}
: see ConstantDDEBifProblem for more information.plotSolution::Any
: user function to plot solutions during continuation. Signature:plotSolution(x, p; kwargs...)
recordFromSolution::Any
:record_from_solution = (x, p; k...) -> norm(x)
function used record a few indicators about the solution. It could benorm
or(x, p) -> x[1]
. This is also useful when saving several huge vectors is not possible for memory reasons (for example on GPU...). This function can return pretty much everything but you should keep it small. For example, you can do(x, p) -> (x1 = x[1], x2 = x[2], nrm = norm(x))
or simply(x, p) -> (sum(x), 1)
. This will be stored incontres.branch
(see below). Finally, the first component is used to plot in the continuation curve.save_solution::Any
: function to save the full solution on the branch. Some problem are mutable (like periodic orbit functional with adaptive mesh) and this function allows to save the state of the problem along with the solution itself. Signaturesave_solution(x, p)
δ::Any
: delta for Finite differences
Methods
getu0(pb)
callspb.u0
getparams(pb)
callspb.params
getlens(pb)
callspb.lens
setparam(pb, p0)
callsset(pb.params, pb.lens, p0)
record_from_solution(pb)
callspb.record_from_solution
Constructors
SDDDEBifProblem(F, delays, u0, params, lens; J, Jᵗ, d2F, d3F, kwargs...)
andkwargs
are the fields above.
Eigen solvers
DDEBifurcationKit.DDE_DefaultEig
— Typemutable struct DDE_DefaultEig{T, Tw, Tv} <: DDEBifurcationKit.AbstractDDEEigenSolver
Default eigen solver for DDEBifurcationKit based on the julia package NonlinearEigenproblems.jl. ore precisely, we rely on NonlinearEigenproblems.iar_chebyshev
for the computation of eigenvalues.
Fields
maxit::Int64
: Default: 100which::Any
: Default: realσ::Any
: Default: 0.0γ::Any
: Default: 1.0tol::Any
: Default: 1.0e-10logger::Int64
: Default: 0check_error_every::Int64
: Default: 1v::Any
: Default: nothing
Constructors
DDE_DefaultEig(; kwargs...)
andkwargs
are the fields above.
Branch switching (branch point)
Missing docstring for continuation(br::ContResult, ind_bif::Int, optionsCont::ContinuationPar ; kwargs...)
. Check Documenter's build log for details.
Branch switching (Hopf point)
Missing docstring for continuation(br::BifurcationKit.AbstractBranchResult, ind_bif::Int, _contParams::ContinuationPar, prob::BifurcationKit.AbstractPeriodicOrbitProblem ; kwargs...)
. Check Documenter's build log for details.
Utils for periodic orbits
Missing docstring for getperiod
. Check Documenter's build log for details.
Missing docstring for getamplitude
. Check Documenter's build log for details.
Missing docstring for getmaximum
. Check Documenter's build log for details.
Misc.
Missing docstring for guess_from_hopf(br, ind_hopf, eigsolver::AbstractEigenSolver, M, amplitude; phase = 0)
. Check Documenter's build log for details.
Missing docstring for get_normal_form
. Check Documenter's build log for details.