  We consider a problem of non-adiabatic dynamics of a 2D fermionic system with
$d+id$-wave symmetry of paring amplitude. Under the mean-field approximation,
we determine the asymptotic behavior of the pairing amplitude following a
sudden change of coupling strength. We also study an extended $d+id$ pairing
system for which the long-time asymptotic states of the pairing amplitude in
the collisionless regime can be determined exactly. By using numerical methods,
we have identified three non-equilibrium steady states described by different
long-time asymptotes of the pairing amplitude for both the non-integrable and
the integrable versions of $d+id$-wave models. We found that despite of its
lack of integrability, long-time dynamics resulting from pairing quenches in
the non-integrable $d+id$ model are essentially similar to the ones found for
its exactly-integrable extended $d+id$ model. We also obtain the long-time
phase diagram of the extended $d+id$ model through the Lax construction that
exploits underlying integrability showing that the dynamic phases obtained by
numerics are consistent with the dynamics of the exactly integrable approach.
Both models describe a topological fermionic system with a topologically
non-trivial BCS phase appearing at weak coupling strength. We show that the
presence of oscillating order parameter region in the chiral $d+id$ pairing
dynamics differs from the d-wave ($d_{x^2-y^2}$), which may be used to probe
pairing symmetries of chiral superconductors.
