  In tokamak plasmas, sheared flows perpendicular to the driving temperature
gradients can strongly stabilize linear modes. While the system is linearly
stable, regimes with persistent nonlinear turbulence may develop, i.e. the
system is subcritical. A perturbation with small but finite amplitude may be
sufficient to push the plasma into a regime where nonlinear effects are
dominant and thus allow sustained turbulence. The minimum threshold for
nonlinear instability to be triggered provides a criterion for assessing
whether a tokamak is likely to stay in the quiescent (laminar) regime. At the
critical amplitude, instead of transitioning to the turbulent regime or
decaying to a laminar state, the trajectory will map out the edge of chaos.
Surprisingly, a quasi-traveling-wave solution is found as an attractor on this
edge manifold. This simple advecting solution is qualitatively similar to, but
simpler than, the avalanche-like bursts seen in earlier turbulent simulations
and provides an insight into how turbulence is sustained in subcritical plasma
systems. For large flow shearing rate, the system is only convectively
unstable, and given a localised initial perturbation, will eventually return to
a laminar state at a fixed spatial location.
