Dynamical Stability and Near-Resonant Architecture of the TOI-2076 Multi-Planet System: An N-Body Study

TOI-2076 is a young, compact multi-planet system whose orbital architecture places its adjacent planets close to low-order mean-motion commensurabilities. We investigate the dynamical stability and near-resonant behaviour of the system using direct N-body simulations with the REBOUND package and the WHFast symplectic integrator. Three independent realizations, initialized with randomized orbital phases, were integrated for t = 2 ×10⁶ yr using a timestep of Δt = 0.5 days. All three realizations remained stable throughout the simulations, with no planetary ejections or collisions. The eccentricities showed bounded oscillations without clear secular growth, with mean standard deviations of \( {\sigma }_{e_{b}}=0.00382, {\sigma }_{e_{c}}=0.00329 \), and \( {\sigma }_{e_{d}}=0.00335 \) for TOI-2076 b, c, and d, respectively. The nominal period ratios are \( \frac{P_{c}}{P_{b}}=1.6577 \) and \( \frac{P_{d}}{P_{c}}=2.0461 \), compared with the exact 5:3 and 2:1 commensurabilities of 1.6667 and 2.0000, respectively. The corresponding resonance angles circulate through the full 0°C–360°C range rather than remaining confined to a bounded libration region, indicating that the simulated configurations remain near-resonant without evidence of resonance locking over the 2 Myr integration. The period ratios also remain nearly constant throughout the simulations, with no systematic evolution toward exact commensurability. Overall, the results show that the adopted TOI-2076 configuration remains dynamically stable over the simulated interval while maintaining a near-resonant, non-librating orbital architecture. These results provide a numerical baseline for future studies using longer integrations and a broader exploration of uncertainties in the planetary orbital and physical parameters.