  The persistent dynamics in systems out of equilibrium, particularly those
characterized by annihilation and creation of topological defects, is known to
involve complicated spatiotemporal processes and is deemed difficult to
control. Here the complex dynamics of defects in active smectic layers exposed
to strong confinements is explored, through self-propulsion of active particles
and a variety of confining geometries with different topology, ranging from
circular, flower-shaped epicycloid, to hypocycloid cavities, channels, and
rings. We identify a wealth of dynamical behaviors during the evolution of
complex spatiotemporal defect patterns as induced by the confining shape and
topology, particularly a perpetual creation-annihilation dynamical state at
intermediate activity with large fluctuations of topological defects and a
controllable transition from oscillatory to damped time correlation of defect
number density via mechanisms governed by boundary cusps. Our results are
obtained by using an active phase field crystal approach. Possible experimental
realizations are also discussed.
