Generalized multistability and noise-induced jumps in a nonlinear dynamical system

A study of the forced Duffing equation is reported, with particular reference to a region of the parameter space where five different attractors coexist. This coexistence, reported in some recent experiments, is called generalized multistability. The role of external noise in bridging the otherwise disjoint basins is explored. Noise-induced couplings are shown to be ruled by simple kinetic equations under a general assumption for the geometry of the boundaries. These kinetic equations yield low-frequency power spectra in qualitative agreement with the experimental results.