# BifurcationKit: PeriodicOrbitOCollProblem Failure to converge with given tolerances

**URL:** https://discourse.julialang.org/t/bifurcationkit-periodicorbitocollproblem-failure-to-converge-with-given-tolerances/123048
**Category:** Modelling & Simulations
**Tags:** question, package
**Created:** [November 25, 2024, 3:26pm UTC](https://discourse.julialang.org/t/bifurcationkit-periodicorbitocollproblem-failure-to-converge-with-given-tolerances/123048 "2024-11-25T15:26:10Z")
**Posts on this page:** 1
**Page:** 1

<div class="post-metadata">

### Author: ![mmplac14](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mmplac14/32/213427_2.png) [@mmplac14](https://discourse.julialang.org/u/mmplac14)
#### Post date: [November 25, 2024, 3:26pm UTC](https://discourse.julialang.org/t/bifurcationkit-periodicorbitocollproblem-failure-to-converge-with-given-tolerances/123048/1 "2024-11-25T15:26:10Z")

</div>

Hello!

I am new to bifurcation analyis and I am working with BifurcationKit to reproduce the bifurcation analysis performed by [Grimbert Faugueras on the Jansen-Rit model](https://www.researchgate.net/publication/252117635_Analysis_of_Jansen's_model_of_a_single_cortical_column).

I have managed to get the continuation graph.

 ![image](https://global.discourse-cdn.com/julialang/original/3X/4/c/4c939a792309d089c55ed8bd42c92db241ef4b98.png)

I also managed to get the periodic orbit starting from the 1st Hopf bifurcation.

 ![image](https://global.discourse-cdn.com/julialang/original/3X/7/0/703827d5e74ec37b07d53e5c47568f6898bff772.png)

Now, I am trying to get the periodic orbits produced by the 2nd Hopf Bifurcation at p = 89. I am using PeriodicOrbitOCollProblem, same as I used to get the graph above. The calculation fails to converge.

```julia
 Error: Failure to converge with given tolerances.
│ We reached the smallest value [dsmin] valid for ds, namely 1.0e-8.
│ Stopping continuation at continuation step 1.
└ @ BifurcationKit ~/.julia/packages/BifurcationKit/RaJtn/src/continuation/Contbase.jl:67
 24.719435 seconds (25.34 M allocations: 20.385 GiB, 20.35% gc time, 45.28% compilation time)

```

I also get logs saying the precision on the FloquetMultiplier is not enough. I have been decreasing the tol\_stability, but these warnings keep appearing.

```julia
┌ Warning: The precision on the Floquet multipliers is 0.01921577015310253.
│ It may be not enough to allow for precise bifurcation detection.
│ Either decrease `tol_stability` in the option ContinuationPar or use a different method than `FloquetColl` for computing Floquet coefficients.
└ @ BifurcationKit ~/.julia/packages/BifurcationKit/RaJtn/src/periodicorbit/Floquet.jl:532

```

Should I be using another type of PeriodOrbit problem? I am confused about when I should be using which.

Do I need to use a different method than FloquetColl? Which one? I have looked at the docs but can’t figure out how to change it and what the other options are.

My code is below. Any pointers would be really appreciated!

```julia
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 = 50.0)

# 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],)

optnewton = NewtonPar(tol = 1e-11, verbose = true)

# continuation options, we limit the parameter range for p
opts_br = ContinuationPar(p_min = -50.0, p_max = 400.0, max_steps = 8000, newton_options = optnewton)
	
# 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 = true, normC = norminf)
	
scene = plot(br, legend=:topleft, ylabel = "y")

print("PERIODIC ORBITS")

# arguments for periodic orbits
# one function to record information and one
# function for plotting
args_po = (	record_from_solution = (x, p; k...) -> begin
		xtt = get_periodic_orbit(p.prob, x, p.p)
		return (max = maximum(xtt[1,:]),
				min = minimum(xtt[1,:]),
				period = getperiod(p.prob, x, p.p))
	end,
	plot_solution = (x, p; k...) -> begin
		xtt = get_periodic_orbit(p.prob, x, p.p)
		arg = (marker = :d, markersize = 1)
		plot!(xtt.t, xtt[1,:]; label = "y0", arg..., k...)
		plot!(xtt.t, xtt[2,:]; label = "y3", arg..., k...)
		plot!(xtt.t, xtt[3,:]; label = "y1", arg..., k...)
        plot!(xtt.t, xtt[4,:]; label = "y4", arg..., k...)
		plot!(xtt.t, xtt[5,:]; label = "y2", arg..., k...)
		plot!(xtt.t, xtt[6,:]; label = "y5", arg..., k...)
		plot!(br; subplot = 1, putspecialptlegend = false)
		end,
	# we use the supremum norm
	normC = norminf)

# continuation parameters
opts_po_cont = ContinuationPar(opts_br, ds= 0.00001, dsmin = 1e-8, dsmax = 0.1,
	max_steps = 100,
	tol_stability = 1e-10)

br_pocoll = @time continuation(
	# we want to branch from the 5th bif. point
	br, 5, opts_po_cont,
	# we want to use the Collocation method to locate PO, with polynomial degree 4
	PeriodicOrbitOCollProblem(60, 4; meshadapt = true);
	# regular continuation options
	normC = norminf,
	args_po...)

br_pocoll

```