Bifurcation theory inverse problem in noisy dynamical systems

Bifurcations in nonlinear systems with weak noise are considered. The local bifurcations are discussed: the saddle-node bifurcation, the transcritical bifurcation, the supercritical and subcritical pitchfork bifurcations. Basing on the known prebifurcational noise rise and saturation phenomena, the inverse problem is introduced: the problem of the bifurcation detection and determining it's type by the observed noise change (noise deviation growth fashion, saturation level, probability density). The inverse problem solution algorithm is suggested. The results obtained open the new ways for designing complex systems diagnostic solutions.