  Carbon nanotubes are devices of choice for investigating the interplay
between electronic transport and nanomechanical motion. In this work, we report
the co-existence of thermal vibrations and large-amplitude self-sustained
oscillations in a carbon nanotube that originates from electron tunneling and
thermal effects. The measured transitions between the two states are described
by a Poisson process, revealing that the interstate switching is induced by
noise. We observe the coexistence of the stable low-amplitude thermal state and
the stable large-amplitude state (limit cycle) over a finite parameter range,
which points to an isola bifurcation. We propose a minimalistic model based on
nonlinear friction to account for the isola. Our work provides evidence for a
new type of bifurcation leading to self-sustained oscillations that largely
differs from the classical Hopf bifurcation, since these large-amplitude
oscillations are a hidden state that can be unveiled via stochastic switching.
We envision that this new dynamical regime and the means to reveal it will be
of interest for various mesoscopic vibrational systems.
