}$. As a result, $s_{y}(k)>0$ for a range of wavevectors, resulting in the unstable growth of density and order parameter fluctuations illustrated in Fig. \[Fig3\]. The fastest growing mode has wave vector $k_{0}=\sqrt{
-s_{2}/2s_{4}}\sim (\rho _{0}-\rho _{c})^{3/2}$. Including the coupling to $\tau_y$ will yield finite Peclet number corrections to the instability. Note that this instability is strongest in the vicinity of the order-disorder transition and is a manifestation of the fact that the dynamics of the system is self regulating, i.e., the control parameter associated with the phase transition, namely the density is dynamically coupled to the emergent ordering that results from the transition through the curvature induced fluxes. This is the dynamics that leads the system to be intrinsically phase separated [@Ramaswamy2003].

![ The banding instability that occurs due to the self-regulating nature of the flow. The striped region is the parameter space in which this instability occurs.[]{data-label="Fig3"}](Fig3.pdf){width="6cm"}

We recall that polar active fluids exhibit a similar instability for wave vectors parallel to the direction of mean order. In that case the mode that goes unstable is a propagating mode and the instability signals the onset of solitary waves consisting of alternating ordered and disordered bands extending in the 