Frequency modulation by perturbation is the essential trait that differentiates limit cycle oscillators from phase oscillators. We studied networks of identical limit cycle oscillators whose frequencies are modulated sensitively by the change of their amplitudes, and demonstrated that the frequencies sustainably take distributed values. We observed two complex phenomena in the networks: stationarily distributed frequencies at a regular interval, and continuous irregular modulation of frequencies. In the analysis we reveal the mechanisms by which the frequencies are distributed, and show how the sensitive modulation of frequencies produces these complex phenomena. We also illustrate the topology of networks regulating the behaviors of the systems.