  Active nematics exhibit spontaneous flows through a well-known linear
instability of the uniformly-aligned quiescent state. Here we show that even a
linearly stable uniform state can experience a nonlinear instability, resulting
in a discontinuous transition to spontaneous flows. In this case, quiescent and
flowing states may coexist. Through a weakly nonlinear analysis and a numerical
study, we trace the bifurcation diagram of striped patterns and show that the
underlying pitchfork bifurcation switches from supercritical (continuous) to
subcritical (discontinuous) by varying the flow-alignment parameter. We predict
that the discontinuous spontaneous flow transition occurs for a wide range of
parameters, including systems of contractile flow-aligning rods. Our
predictions are relevant to active nematic turbulence and can potentially be
tested in experiments on either cell layers or active cytoskeletal suspensions.
