  Much of the physical world around us can be described in terms of harmonic
oscillators in thermodynamic equilibrium. At the same time, the far from
equilibrium behavior of oscillators is important in many aspects of modern
physics. Here, we investigate a resonating system subject to a fundamental
interplay between intrinsic nonlinearities and a combination of several driving
forces. We have constructed a controllable and robust realization of such a
system using a macroscopic doubly clamped string. We experimentally observe a
hitherto unseen double hysteresis in both the amplitude and the phase of the
resonator's response function and present a theoretical model that is in
excellent agreement with the experiment. Our work provides a thorough
understanding of the double-hysteretic response through a symmetry breaking of
parametric phase states that elucidates the selection criteria governing
transitions between stable solutions. Our study motivates applications ranging
from ultrasensitive force detection to low-energy computing memory units.
