Overstable resonance capture of a two-planet system with convergent migration. The planet and disk parameters are m_i=1 M_⊕, m_o=10 M_⊕, τ_m=8 × 10⁵ yr and τ_m/τ_e = 10³. By t≃3 × 10⁴ yr, the planets become trapped in a 2:1 MMR. The inner planet’s eccentricity rapidly excites to 0.02, followed by oscillations with significant amplitude, while the resonant angle exhibits similar behavior. In phase space, the trajectory initially evolves toward a resonant equilibrium point (black dot) before stabilizing into a limit cycle around this point. We term this phenomenon–where the system remains trapped by librating around an equilibrium with the finite amplitude–an overstable trap. See https://github.com/llh-astro/resonance/raw/main/gif/overstable_trap.gif