Library

struct 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 a BifFunction. For more information, please look at the website https://bifurcationkit.github.io/DDEBifurcationKit.jl/dev/BifProblem

• delays::Any: function delays. It takes the parameters and return the non-zero delays in an AbstractVector form. Example: delays = par -> [1.]

• u0::Any: Initial guess

• delays0::Any: initial delays (set internally by the constructor)

• params::Any: parameters

• lens::Union{typeof(identity), Nothing, IndexLens, PropertyLens, ComposedFunction}: Typically a Accessors.@optic. It specifies which parameter axis among params is used for continuation. For example, if par = (α = 1.0, β = 1), we can perform continuation w.r.t. α by using lens = (@optic _.α). If you have an array par = [ 1.0, 2.0] and want to perform continuation w.r.t. the first variable, you can use lens = (@optic _[1]). For more information, we refer to Accessors.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 be norm 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 in contres.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. Signature save_solution(x, p)

• δ::Any: delta for Finite differences

Methods

• getu0(pb) calls pb.u0
• getparams(pb) calls pb.params
• getlens(pb) calls pb.lens
• setparam(pb, p0) calls set(pb.params, pb.lens, p0)
• record_from_solution(pb) calls pb.record_from_solution

Constructors

• ConstantDDEBifProblem(F, delays, u0, params, lens; J, Jᵗ, d2F, d3F, kwargs...) and kwargs are the fields above.

struct 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 a BifFunction. For more information, please look at the website https://bifurcationkit.github.io/DDEBifurcationKit.jl/dev/BifProblem

• delays::Any: function delays. It takes the parameters and the state and return the non-zero delays in an AsbtractVector form. Example: delays = (par, u) -> [1. + u[1]^2]

• u0::Any: Initial guess

• delays0::Any: initial delays (set internally by the constructor)

• params::Any: parameters

• lens::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 be norm 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 in contres.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. Signature save_solution(x, p)

• δ::Any: delta for Finite differences

Methods

• getu0(pb) calls pb.u0
• getparams(pb) calls pb.params
• getlens(pb) calls pb.lens
• setparam(pb, p0) calls set(pb.params, pb.lens, p0)
• record_from_solution(pb) calls pb.record_from_solution

Constructors

• SDDDEBifProblem(F, delays, u0, params, lens; J, Jᵗ, d2F, d3F, kwargs...) and kwargs are the fields above.

mutable 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: 100

• which::Any: Default: real

• σ::Any: Default: 0.0

• γ::Any: Default: 1.0

• tol::Any: Default: 1.0e-10

• logger::Int64: Default: 0

• check_error_every::Int64: Default: 1

• v::Any: Default: nothing

Constructors

• DDE_DefaultEig(; kwargs...) and kwargs are the fields above.