Invariance of Frequency Difference in Nonresonant Entrainment of Detuned Oscillators Induced by Common White Noise

Abstract

We studied the entrainment of two uncoupled detuned limit cycle oscillators subjected to a common external white Gaussian noise. We found a novel type of entrainment behavior for a general class of oscillators: as noise intensity increases, the phases of the two oscillators come to be almost always locked with each other although there is no frequency locking in the sense that the mean frequency difference remains the same as the natural frequency difference. We also show that a common noise induces a macroscopic oscillation with no frequency locking in a population of detuned oscillators.