Get periodic orbit for system of ODEs with fixed parameters

[AngelicaP1998]

How can I use get_periodic_orbits and getperiod to get the periodic orbit and period of my system, given a specific set of parameters?

function F!(du, u, p, t)
    x, y = u                 
    @unpack ω1, ω2 = p         
    du[1] = ω1 * y            
    du[2] = -ω2 * x           
end

@with_kw mutable struct Params
    ω1::Float64 = 2pi
    ω2::Float64 = 2pi
end

par = Params()
u0 = [0., 1.]

[rveltz]

Your linear system has an infinite number of periodic orbits. It is very singular.

[AngelicaP1998]

Thank you! In general, for a system with just one periodic orbit, what should I do?

[rveltz]

it depends if it born at a hopf point (see here) or you have an estimate of the orbit (see here)