A direct dynamical test of the sunspot cycle is carried out to indicate that a stochastically forced nonlinear oscillator characterizes its dynamics. The sunspot series is then decomposed into its eigen time-delay coordinates. The relevant analysis reveals that the sunspot series exhibits bistability, with the possibility of modeling the solar cycle as a stochastically and periodically forced bistable oscillator, accounting for poloidal and toroidal modes of the solar magnetic field. Such a representation enables us to conjecture stochastic resonance as the key mechanism in amplifying the planetary influence on the Sun, and that extreme events, due to turbulent convection noise inside the Sun, dictate crucial phases of the sunspot cycle, such as the Maunder minimum.