Issues with continuation in BifurcationKit

New to Julia
1

Hi!

I am new to Julia and BifurcationKit. I am trying to perform a bifurcation analysis of the Jansen-Rit model as was done by Grimbert and Faugueras but I keep running into this error when calling continuation

The function iterate_from_two_points exists, but no method is defined for this combination of argument types.
Closest candidates are:
  iterate_from_two_points(::ContIterable, ::Any, ::T, ::Any, !Matched::T; _verbosity) where T
   @ BifurcationKit ~/.julia/packages/BifurcationKit/RaJtn/src/Continuation.jl:382

I have tried some of the tutorials on the BifurcationKit website, but this steps works fine. I am using Jupyter Notebook in VSCode if it makes a difference. If someone could provide some guidance I would greatly appreciate it!

Here is the full code:

using Revise, Plots
using BifurcationKit

const BK = BifurcationKit

# Define the function σ
function σ(v, e0 = 2.5, v0 = 6, r=0.56)
    2 * e0 / (1 + exp(r * (v0 - v)))
end

# vector field
function jansenrit(z, param)
	(;A, a, B, b, C1, C2, C3, C4, p) = param
	y0, y3, y1, y4, y2, y5 = z
	[
	    y3
        A * a * σ(y1 - y2) - 2 * a * y3 - a^2 * y0
        y4
        A * a * (p + C2 * σ(C1 * y0)) - 2 * a * y4 - a^2 * y1
        y5
        B * b * C4 * σ(C3 * y0) - 2 * b * y5 - b^2 * y2
	]
end

# parameter values
C= 135
par = (A = 3.25, a = 100, B = 22, b = 50, C1 = C, C2 = 0.8 * C, C3 = 0.25 * C, C4 = 0.25 * C, p = 50)

# initial condition
z0 = [0.0, 0.0, 15.0, 0.0, 10.0, 0.0]

# Bifurcation Problem
prob = BifurcationProblem(jansenrit, z0, par, (@optic _.p);
	record_from_solution = (x, p; k...) -> (y0 = x[1], y3 = x[2], y1 = x[3], y4 = x[4], y2 = x[5], y5 = x[6]),)

opts_br = ContinuationPar(p_min =1.0, p_max = 400.0)

# continuation options, we limit the parameter range for p
opts_br = ContinuationPar(p_min =1.0, p_max = 400.0)

# continuation of equilibria
br = continuation(prob, PALC(), opts_br;
	# we want to compute both sides of the branch of the initial
	# value of p = 100
	bothside = false, verbosity = 3)
2

it is because par.p is an Int. Use par = (A = 3.25, a = 100, B = 22, b = 50, C1 = C, C2 = 0.8 * C, C3 = 0.25 * C, C4 = 0.25 * C, p = 50.0)

1 Like
3

Thank you Romain! Now I am confused about how to set the range for p. Even though I have set p_min =0.0 and p_max =400.0, it only goes from 50 to ~110. I assume the 50 comes from the initial parameter values set in ‘par’. I have tried different settings for dsmax, ds_min, ds but I can only increase the range so much.

# continuation options, we limit the parameter range for p
opts_br = ContinuationPar(p_min =0.0, p_max = 400.0, dsmax = 2.0, dsmin= 0.001, ds = 0.001, max_steps = 1000)

# continuation of equilibria
br = continuation(prob, PALC(), opts_br;
	# we want to compute both sides of the branch of the initial
	# value of p = 100
	bothside = false, verbosity = 3)

image
image1200×804 18 KB

4

br does not contain 1000 points? What is the last continuation step printed in the REPL?

5

No, it only had 308 points. I managed to fix it though by lowering the Newton tolerance to e-9. Now I am able to get to the max_steps I specify.

Do you think it might have been failing to converge before? It wasn’t logging anything apart from a “5-element Vector{ComplexF64}” (I don’t know what this vector is) so it is difficult to say what was happening.

6

You can tell this by passing NewtonPar(verbose = true). You can also use the normC = norminf instead of the 2-norm. Please tell us if this is newton tolerance that was too small.

7

Is doing normC = norminf equivalent to passing NewtonPar(verbose = true)? The outputs seems slightly different, but it does seem like tolerance is the issue

With normC = norminf:

image
image1906×244 46.7 KB

And with NewtonPar(verbose = true):

image
image1770×122 22.2 KB

8

Hi

No NewtonPar contains the newton parameters. Above you just specify that you want newton to output it’s iterations.

But judging from your screenshots, you don’t see them. Are you using Pluto.jl?

9

basically, I was suggesting to do


br = continuation(prob, PALC(), ContinuationPar(opts_br, newton_options = NewtonPar(tol = 1e-11, verbose = true));
	# we want to compute both sides of the branch of the initial
	# value of p = 100
        normC = norminf,
	bothside = false, verbosity = 3)
10

Hey!

The iterations get printed but not always, perhaps because I am using a Jupyter Notebook.

image
image960×1126 30.4 KB

Do you recommend Pluto?

11

Ah that’s why. I use vscode where all iterations are printed.

12

I do not use pluto