Help with continuation using BifurcationKit.jl

Specific Domains Numerics
1

Hello all,

Relatively new to BifurcationKit (I have used other continuation software in the past). I’ve been able to get a 2D system (quite similar to the 3D system I’m having trouble with) to work, so any help or advice would be welcome.

The sample code is:

using Revise
using Plots, Setfield
using BifurcationKit
const BK = BifurcationKit
gr()

# vector field
function ODE_3D(u, p)
    (;A1,A2,A3,B1,B2,B3,mu12,mu21,mu31,mu32,mu33,
        K1,K2,K3,K4,K5,Tr_mom,Tr_cyt,x_tot,y_tot) = p
    x, y, z = u
    out = similar(u)
    out[1] = A1 - B1*x + mu12*K1/(K1 + y) + Tr_mom*(x_tot - x) - Tr_cyt*x
    out[2] = A2 - B2*y + mu21*K2/(K2 + x) + Tr_mom*(y_tot - y) - Tr_cyt*y
    out[3] = A3 - B3*z + mu31*x/(K3 + x) + mu32*K4/(K4 + y) - mu33*z^2/(K5^2 + z^2)
    out
end 

# Model parameters
params = (A1 = 0, A2 = 9127.71, A3 = 44178.2,
    B1 = 0.5796, B2 = 0.1205, B3 = 0.347,
    mu12 = 2.76873, mu21 = 2.14908, mu31 = 0.586803, mu32 = 0.907841, mu33 = 2.13773,
    K1 = 0.0615, K2 = 0.0615, K3 = 0.0116, K4 = 0.0219, K5 = 0.0143,
    Tr_mom = 1.16e-2, Tr_cyt = 1.16e-3, x_tot = 16850, y_tot = 7000)

record3D(x, p; k...) = (x = x[1], y = x[2], z = x[3])

# Initial conditions
u0 = [329.9683, 69104.8357, 127310.2278];

prob = BifurcationProblem(ODE_3D, u0, params, (@optic _.A1); record_from_solution = record3D)

# Continuation parameters
opts_br = ContinuationPar(
    dsmin = 1e-9,           # Minimum step size
    dsmax = 1e-3,           # Maximum step size
    ds = 1e-6,              # Initial step size
    p_min = 0.0,            # Minimum value of the parameter
    p_max = 100.0,          # Maximum value of the parameter
    max_steps = 1e6,        # Maximum number of continuation steps
    tol_stability = 1e-12,  # Tolerance for stability computation
    detect_fold = true,     # Detect fold bifurcations
    detect_bifurcation = 1  # Number of bifurcation detection methods
)

br = continuation(prob, PALC(), opts_br, bothside = true, normC = norminf)

The following error is generated

MethodError: no method matching iterate_from_two_points(::ContIterable{BifurcationKit.EquilibriumCont, BifurcationProblem{BifFunction{typeof(ODE_3D), BifurcationKit.var"#8#24", Nothing, BifurcationKit.var"#6#22", Nothing, BifurcationKit.var"#11#28"{BifurcationKit.var"#d1Fad#26"}, BifurcationKit.var"#13#30", BifurcationKit.var"#15#32", BifurcationKit.var"#17#34", Bool, Float64}, Vector{Float64}, @NamedTuple{A1::Int64, A2::Int64, A3::Int64, B1::Float64, B2::Float64, B3::Float64, mu12::Float64, mu21::Float64, mu31::Float64, mu32::Float64, mu33::Float64, K1::Float64, K2::Float64, K3::Float64, K4::Float64, K5::Float64, Tr_mom::Float64, Tr_cyt::Float64, x_tot::Int64, y_tot::Int64}, PropertyLens{:A1}, typeof(BifurcationKit.plot_default), typeof(record3D), typeof(BifurcationKit.save_solution_default)}, PALC{Secant, MatrixBLS{DefaultLS}, Float64, BifurcationKit.DotTheta{BifurcationKit.var"#279#281", BifurcationKit.var"#280#282"}}, Float64, DefaultLS, DefaultEig{typeof(real)}, typeof(norminf), typeof(BifurcationKit.finalise_default), typeof(BifurcationKit.cb_default), Nothing}, ::Vector{Float64}, ::Int64, ::Vector{Float64}, ::Float64; _verbosity::UInt8)

Closest candidates are:
  iterate_from_two_points(::ContIterable, ::Any, ::T, ::Any, ::T; _verbosity) where T
   @ BifurcationKit ~/.julia/packages/BifurcationKit/KwA2l/src/Continuation.jl:382

I’ve tried a number of fixes without any success

  • Perform the continuation in one direction
  • Use the default continuation parameters
  • Alternative continuation algorithms
  • I’ve checked that the continuation is close to the steady state

Thanks

2

A1 is an Int in params and BK does not know to what it should convert it.
Given the range of values, you may have to adjust the newton tolerance @reset opts_br.newton_options.tol = new_wanted_tolerance