We analyze a large dynamical system of limit-cycle oscillators with mean-field coupling and randomly distributed natural frequencies. Depending on the choice of coupling strength and the spread of natural frequencies, the system exhibits frequency locking, amplitude death, and incoherence, as well as novel unsteady behavior characterized by periodic, quasiperiodic, or chaotic evolution of the system’s order parameter. The phase boundaries between several of these states are obtained analytically.

• Received 26 March 1990

DOI:https://doi.org/10.1103/PhysRevLett.65.1701