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We formulate a reduction theory that describes the response of an oscillatornetwork as a whole to external forcing applied nonuniformly to its constituentoscillators. The phase description of multiple oscillator networks coupledweakly is also developed. General formulae for the collective phase sensitivityand the effective phase coupling between the oscillator networks are found. Ourtheory is applicable to a wide variety of oscillator networks undergoingfrequency synchronization. Any network structure can systematically be treated.A few examples are given to illustrate our theory.

Collective dynamical response of coupled oscillators with any network structure