You can easily debug these errors by going verbose like opt_newton = NewtonPar(tol = 1e-12, maxIter = 10, verbose = true)

Also, you cannot pass recordFromSolution to codim 2 (you could but you have to dispatch it on BorderedArrays), hence

hp_codim2 = continuation(br, 1, (@lens _.k1),
ContinuationPar(opts_br, pMin = -0.5, pMax = 0.5,
ds = -0.001, dsmax = 0.05) ;
normC = norminf,
# detection of codim 2 bifurcations with bisection
detectCodim2Bifurcation = 2,
# tell to start the Hopf problem using eigen elements: compute left eigenvector
startWithEigen = true,
# we update the Hopf problem at every continuation step
updateMinAugEveryStep = 1,
# compute both sides of the initial condition
bothside = true,
)

Thank you
I get the following result, and as I understand it, it is incorrect because real numbers of eigenvalues not zero, perhaps this is due to accuracy

You can have access to more than what is given by show(nf) by looking at the fields of nf where nf is the normal form nf = getNormalForm(br, ind::Int).

In a nutshell, I try to test as much as I can to test the code against analytics although the above tests are not perfect because they do not involve the computatation of the center manifold since it is the whole space. But that’s already a test ;D

I am happy to know of a bug here because it will become one less in the package

Okay, thank you. I wonder what this may indeed be a bautin bifurcation. I test critical parametres and see next attractor. the Lyapunov spectrum and the eigenvalues indicate that this is indeed a bautin bifurcation if of course believe the results of the calculation. Before critical value i have not zero real numbers but i have zero largest lyapunov exponent.
for calculate fixed point and spectrum uses DynamicalSystems.jl

perhaps this is so, I hardly understand what is happening in the system, because there is only one state of equilibrium, which practically does not affect the dynamics in any way
I’ll attach another projection. perhaps you know what it is