Conditional Lyapunov Exponent Depending on Spectrum of Input Noise in Common-Noise-Induced Synchronization

Abstract

We study the synchronization of dynamical systems induced by common additional external colored noise. In particular, we consider the special case that the external input noise is generated by a linear second-order differential equation forced by Gaussian white noise. So the frequency spectrum of this noise is not constant. In the case that noise-free dynamics is chaotic, we find examples where the synchronization is enhanced when the peak of the input noise is close to the peak of the noise-free dynamics in frequency space. In the case that noise-free dynamics is non-chaotic, we do not observe this phenomenon.