  We consider a nonequilibrium transition that leads to the formation of
nonlinear steady-state structures due to the gas flow scattering on a partially
penetrable obstacle. The resulting nonequilibrium steady state (NESS)
corresponds to a two-domain gas structure attained at certain critical
parameters. We use a simple mean-field model of the driven lattice gas with
ring topology to demonstrate that this transition is accompanied by the
emergence of local invariants related to a complex composed of the obstacle and
its nearest gas surrounding, which we refer to as obstacle edges. These
invariants are independent of the main system parameters and behave as local
first integrals, at least qualitatively. As a result, the complex becomes
insensitive to the noise of external driving field within the overcritical
domain. The emerged invariants describe the conservation of the number of
particles inside the obstacle and strong temporal synchronization or
correlation of gas states at obstacle edges. Such synchronization guarantees
the equality to zero of the total edge current at any time. The robustness
against external drive fluctuations is shown to be accompanied by strong
spatial localization of induced gas fluctuations near the domain wall
separating the depleted and dense gas phases. Such a behavior can be associated
with nonequilibrium protection effect and synchronization of edges. The
transition rates between different NESSs are shown to be different. The
relaxation rates from one NESS to another take complex and real values in the
sub- and overcritical regimes, respectively. The mechanism of these transitions
is governed by the generation of shock waves at the back side of the obstacle.
In the subcritical regime, these solitary waves are generated sequentially many
times, while only a single excitation is sufficient to rearrange the system
state in the overcritical regime.
