Although numerous strategies are now available to generate rudimentary forms of synthetic cell-like entities, minimal progress has been made in the sustained excitation of artificial protocells under non-equilibrium conditions. Here we demonstrate that the electric field energization of coacervate microdroplets comprising polylysine and short single strands of DNA generates membrane-free protocells with complex, dynamical behaviours. By confining the droplets within a microfluidic channel and applying a range of electric field strengths, we produce protocells that exhibit repetitive cycles of vacuolarization, dynamical fluctuations in size and shape, chaotic growth and fusion, spontaneous ejection and sequestration of matter, directional capture of solute molecules, and pulsed enhancement of enzyme cascade reactions. Our results highlight new opportunities for the study of non-equilibrium phenomena in synthetic protocells, provide a strategy for inducing complex behaviour in electrostatically assembled soft matter microsystems and illustrate how dynamical properties can be activated and sustained in microcompartmentalized media.