  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.
