Left panel: evolutionary trajectory of a Type-F particle associated with Set 3 of N-body simulations in the (Ω₂, i₂) plane (black curve). The initial orbital parameters of this particle are a₂ = 23.580 au, e₂ = 0.331, i₂ = 72.326°, ω₂ = 134.249°, and Ω₂ = 247.646°. The values of a₁ and e₁ of the inner Jupiter-mass planet of the system are 1.333 au and 0.566, respectively. The red and blue curves illustrate the separatrix and the pairs (Ω₂, i₂) that vanish the ω₂ quadrupole precession rate for an inner perturber of e₁ = 0.566, respectively. Right panel: temporal evolution of the argument of pericenter ω₂ of such a particle.