Controlling coherence of noisy and chaotic oscillators by a linear feedback

We analyze the dynamics of a noisy limit cycle oscillator coupled to a general passive linear system. We analytically demonstrate that the phase diffusion constant, which characterizes the coherence of the oscillations, can be efficiently controlled. Theoretical analysis is performed in the framework of linear and Gaussian approximations and is supported by numerical simulations. We also demonstrate numerically the coherence control of a chaotic system.