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The linear response is studied in globally coupled oscillator systemsincluding the Kuramoto model. We develop a linear response theory which can beapplied to systems whose coupling functions are generic. Based on the theory,we examine the role of asymmetry introduced to the natural frequencydistribution, the coupling function, or the coupling constants. A remarkabledifference appears in coexistence of the divergence of susceptibility at thecritical point and a nonzero phase gap between the order parameter and theapplied external force. The coexistence is not allowed by the asymmetry in thenatural frequency distribution but can be realized by the other two types ofasymmetry. This theoretical prediction and the coupling-constant dependence ofthe susceptibility are numerically verified by performing simulations in$N$-body systems and in reduced systems obtained with the aid of theOtt-Antonsen ansatz.

A role of asymmetry in linear response of globally coupled oscillator systems