Prebifurcation noise amplification and noise-dependent hysteresis as indicators of bifurcations in nonlinear geophysical systems

Abstract

Abstract. The phenomena of prebifurcation noise amplification and noise-dependent hysteresis are studied as prospective indicators of bifurcations ("noisy precursor") in nonlinear Geophysical systems. The phenomenon of prebifurcation noise amplification arises due to decreasing of damping coefficients just before bifurcation. A simple method for the estimation of the forced fluctuation variance is suggested which is based on results of linear theory up to the boundary of its validity. The upper level for the fluctuation variance before the onset of the bifurcation is estimated from the condition that the contribution of the non-linear term becomes comparable (in the sense of mean squares) with that of the linear term. The method has proved to be efficient for two simple bifurcation models (period doubling bifurcation and pitchfork bifurcation) and might be helpful in application to geophysics problems. The transition of a nonlinear system through the bifurcation point offers a new opportunity for estimating the internal noise using the magnitude of the noise-dependent hysteretic loop, which occurs when the control parameter is changed in the forward and backward direction.