Noise-induced triggering in low-density jets*

We study the effect of white Gaussian noise on a low-density axisymmetric jet in the hysteretic bistable regime produced by a subcritical Hopf bifurcation. We find that noise can induce triggering, causing the jet to transition from a linearly stable fixed point to a stable periodic limit cycle. When the noise amplitude increases, the Hopf and saddle-node points move towards each other, decreasing the width of the bistable region. This decrease is approximately linear, which we attribute to the near-linear behavior of the amplitude of the unstable limit cycle between the Hopf and saddle-node points. When the noise amplitude is sufficiently high, the bistable region vanishes altogether, causing the subcritical bifurcation to appear like a supercritical bifurcation. We conclude by showing that these triggering dynamics can be accurately reproduced with a noise-driven van der Pol (VDP) oscillator.