Intermittency in relation with 1/f noise and stochastic differential equations

Abstract: One of the models of intermittency is on-off intermittency, arising due to time-dependent forcing of a bifurcation parameter through a bifurcation point. For on-off intermittency the power spectral density of the time-dependent deviation from the invariant subspace in a low frequency region exhibits 1/\sqrt{f} power-law noise. Here we investigate a mechanism of intermittency, similar to the on-off intermittency, occurring in nonlinear dynamical systems with invariant subspace. In contrast to the on-off intermittency, we consider the case where the transverse Lyapunov exponent is zero. We show that for such nonlinear dynamical systems the power spectral density of the deviation from the invariant subspace can have 1/f^\beta form in a wide range of frequencies. That is, such nonlinear systems exhibit 1/f noise. The connection with the stochastic differential equations generating 1/f^\beta noise is established and analyzed, as well.