Instability conjecture for traveling waves with decreasing myosin mass

Let $M$ denote the total myosin mass of a traveling wave solution and let $V$ denote its velocity. Consider parameter ranges in which $M$ decreases as a function of $V$ for small $V$. Instability conjecture. In this range, the traveling wave solutions are nonlinearly unstable. The conjecture concerns the stability change associated with the observed subcritical pitchfork bifurcation; the source states that a rigorous proof is forthcoming.