Relationship between $(\frac{e_{min}}{e_c}{)}^2$ and the resonance order k under different migration rates ȧ_N. The horizontal axis represents k, and the vertical axis represents the value of $(\frac{emin}{e_c}{)}^2$. Different colors indicate different ȧ_N, and the lines represent the fitting results based on Eqs. (1) and (2) for the corresponding ȧ_N. Cross marks denote the 1: q MMRs. The purple squares represent the validation set for the fit, and these MMRs were recorded with more than ten particles only when ȧ_N = 0.01 au/Myr.