  We demonstrate that several nonvariational continuum models commonly used to
describe active matter as well as other active systems exhibit nongeneric
behavior: each model supports asymmetric but stationary localized states even
in the absence of pinning at heterogeneities. Moreover, such states only begin
to drift following a drift-transcritical bifurcation as the activity increases.
Asymmetric stationary states should only exist in variational systems, i.e., in
models with gradient structure. In other words, such states are expected in
passive systems, but not in active systems where the gradient structure of the
model is broken by activity. We identify a "spurious" gradient dynamics
structure of these models that is responsible for this nongeneric behavior, and
determine the types of additional terms that render the models generic, i.e.,
with asymmetric states that appear via drift-pitchfork bifurcations and are
generically moving. We provide detailed illustrations of our results using
numerical continuation of resting and steadily drifting states in both generic
and nongeneric cases.
