Use SteadyStateProblem

[oameye]

It can be a good idea to use SteadyStateProblem in the equilib function instead of Callback in combination with ODEProblem. In the background this will be basically be the same as now, however, it will give probably better warning, output, retcode. A benchmark/comparison is here in order.

CriticalTransitions.jl/src/systemanalysis/stability.jl

Lines 15 to 29 in 105ef80

	function equilib(sys::StochSystem, state::State;
	dt=0.01,
	tmax=1e5,
	abstol=1e-5,
	solver=Euler())
	condition(u, t, integrator) = norm(integrator.uprev-u) < abstol
	affect!(integrator) = terminate!(integrator)
	equilib_cond = DiscreteCallback(condition, affect!)
	prob = ODEProblem(sys.f, state, (0, tmax), p(sys))
	sol = solve(prob, solver; dt=dt, callback=equilib_cond, save_on=false, save_start=false)
	sol.u[1]
	end;

[reykboerner]

We were actually considering to remove the equilib function altogether. With Attractors.jl or fixedpoints in ChaosTools.jl there are much better ways to find attractors and equilib as written above is just prone to stop in quasi-equilibria.

[oameye]

I think keeping it is still very useful, but I agree we should add more methods, which is just the writing interface for Stochsystem which in the background juts translates to CoupledODEs struct

In HarmonicBalance.jl use a method called homotopyContinuation which guarantees to find all critical points (attractors, repellers and saddle nodes). It has been very effective for us. However, something like this would be more useful for attractors.jl.