Absolute and convective instabilities in nonlinear systems

The concepts of absolute and convective instability are extended to nonlinear systems with broken Galilean invariance. As an illustrative model we describe the behavior of a flow, homogeneous in a semi-infinite domain, which undergoes a subcritical pitchfork bifurcation. The classical bifurcation phenomenology is shown to be nontrivially affected by the presence of a nonremovable advection term. In particular the existence of a hysteresis loop is shown to be restricted to the nonlinear absolute instability range. A qualitative description of the possible scenarios likely to arise in subcritically bifurcating open flows is outlined and a practical test is suggested to determine the nature of the bifurcation.