“…Considering sym-metric interaction in the dynamics is only an approximation that may simplify theoretical analysis, but which may fail to capture important phenomena occurring in real systems. For example, asymmetric interaction leads to novel features such as families of travelling wave states 13,14 , glassy states and super-relaxation 15 , and so forth, and has been invoked to discuss coupled circadian neurons 16 , dynamic interactions 17,18 , etc. A generalization of the Kuramoto model (1) that accounts for asymmetric interaction is the so-called Sakaguchi-Kuramoto model, with the dynamics described by the equation of motion 19 dθ…”