Fluctuations in nonlinear systems near bifurcations corresponding to the appearance of new stable states

Fluctuations in nonlinear multidimensional dynamical systems caused by outer δ-correlated random forces are considered. The slowness of one of the motions at parameter values within the bifurcation region allows us to use the adiabatic approximation and hence to reduce the multidimensional problem to a one-dimensional problem. The exponent and the pre-exponential factor in the expression for the probability of the transition from the metastable equilibrium state of the system are calculated. The kinetics of fluctuations in the systems that are near the bifurcation point where two stable states coincide is considered. The results are illustrated with an example of the Duffing nonlinear oscillator in an external resonance field.