Organisms can be synchronized not only to the natural 24-h light-dark cycle but also to artificial non-24-h cycles. Interestingly, when the period of the cycle is far from 24 h, organisms may show complicated behavioral patterns. For example, exposed to a 22-h light-dark cycle, in behavioral activity of rats, a phenomenon called "dissociation" emerges, i.e., one periodic component shows a 22-h period and the other shows a period close to the endogenous period of the animal (around 24 h). It has been found that these two components are regulated by two subgroups of the suprachiasmatic nucleus (SCN), respectively, with the ventrolateral part regulating the 22-h component and the dorsomedial part regulating the other component. In the present study, based on a mathematical model, we will examine how the ratio of amplitudes between these two subgroups affects the entrainment of the SCN to the external 22-h light-dark cycle. Our results show that the dissociation happens when the ratio is smaller than 1 and the maximal entrainment (synchronization) ability of the SCN to the external cycle is obtained when the ratio is larger than 1. Our finding sheds light on the dissociation between the subgroups and suggests that the heterogeneity in the amplitudes alter the entrainment ability of the SCN.