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A diversity of resonance configurations may be formed under the different migration of two giant planets. Researchers have shown that the HD 128311 and HD 73526 planetary systems are involved in a  2 : 1  mean motion resonance but not in apsidal corotation, because one of the resonance arguments circulates over the dynamical evolution. In this paper, we investigate potential mechanisms to form the  2 : 1  librating–circulating resonance configuration.  In the late stage of planetary formation, scattering or colliding among planetesimals and planetary embryos can frequently occur. Hence, in our model, we consider a planetary configuration of two giants together with few terrestrial planets. We find that both colliding or scattering events at a very early stage of dynamical evolution can influence the configurations trapped into resonance. A planet–planet scattering of a moderate terrestrial planet, or multiple scattering of smaller planets in a crowded planetary system can change the resonant configuration. In addition, collision or merging can alter the masses and locations of the giant planets, which also play an important role in shaping the resonant configuration during the dynamical evolution. In this sense, the librating–circulating resonance configuration is more likely to form by a hybrid mechanism of scattering and collision.

A hybrid mechanism forming a 2:1 librating–circulating resonant configuration in the planetary system