The Sakaguchi-Kuramoto model is a modification of the well-known Kuramoto\nmodel, in which a frustration factor is added to the coupling term of\neach phase oscillator. The added frustration factor destroys the gradient\nstructure, but the modified model is more widely used in practice. In this paper,\nwe study how frustration factors influence the synchronization transition\nof coupled oscillators in the Sakaguchi-Kuramoto model with frequency\nmismatch rules. The results show that in the system of coupled oscillators, the\nfrustration factor manifests a disorder field, which restrains the explosive\nsynchronization and weakens the synchronization ability of the whole network.\nIn addition, it is found that the frequency synchronization can not be\ndetected by the common phase order parameter, so a new index is introduced\nto characterize the degree of frequency synchronization. As an example, at\nthe end of the paper, we theoretically analyze the synchronization dynamics\nof two-oscillator system, and indirectly verify the correctness of simulations\nfor the multi-body system.
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