Hi all! I’m trying to recreate a continuation figure from a paper using the package BifurcationKit.jl, and so far have done okay for the equilibrium solutions. However, now I’m trying to continue the periodic solutions, and I’ve run into this warning that I haven’t been able to get rid of (I’m using PeriodicOrbitTrapProblem):

```
┌ Error: The amplitude for the predictor for the first periodic orbit on the bifurcated branch is not small 0.09068714864783184.
You can either decrease `ds`, or specify how far `δp` from the bifurcation point you want the branch of periodic orbits to start.
Alternatively, you can specify a multiplicative factor `ampfactor` to be applied to the predictor
└ @ BifurcationKit
```

Which creates a bifurcation diagram like so (the periodic orbit is in yellow):

And here are my parameters… there’s a lot going on and I’ve already tried to decrease ds, but it doesn’t really help. What does the warning mean when it says ‘The amplitude for the predictor for the first periodic orbit on the bifurcated branch is not small’?

```
# HAVING ISSUES WITH AMPLITUDE of PO or SOMETHING!
par = (ϵ = 0.05, θ = 0.5, wₛ = 1.0, wₘ = -0.7, wₜ = 0.0, wₚ = 0.38340498)
y0 = [1.000665065783716, -0.20354471737248953, 0.1887856422707109]
# bifurcation problem
prob = BifurcationProblem(CTRNN3D!, y0, par,
# specify the continuation parameter
(@lens _.wₚ), record_from_solution = recordFromSolution)
# newton parameters
optn_po = NewtonPar(tol = 1e-8, max_iterations = 25)
# continuation parameters
opts_po_cont = ContinuationPar(dsmax = 0.1, ds= 0.01, dsmin = 1e-4,
newton_options = (@set optn_po.tol = 1e-8), tol_stability = 1e-2, detect_bifurcation = 1)
Mt = 101 # number of time sections
args_po = ( record_from_solution = (x, p) -> 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)
Plots.plot!(xtt.t, xtt[1,:]; label = "y₁", arg..., k...)
Plots.plot!(xtt.t, xtt[2,:]; label = "y₂", arg..., k...)
Plots.plot!(xtt.t, xtt[3,:]; label = "y₃", arg..., k...)
Plots.plot!(br; subplot = 1, putspecialptlegend = false)
end,
# we use the supremum norm
normC = norminf)
br_potrap = BifurcationKit.continuation(
# we want to branch form the 3rd bif. point
br, hopf_ind, opts_po_cont,
# we want to use the Trapeze method to locate PO
PeriodicOrbitTrapProblem(M = Mt);
args_po...,
)
```

For context, I couldn’t get the code running unless I followed tutorials very closely, my particular code is mostly adapted from: Neural Mass Equation (Hopf aBS)

Thank you so much for your help in advance, all of this is really new to me so I apologise if I’ve missed something obvious!