One embodiment of the present invention is a unique pulse detonation combustion system. Another embodiment is a unique gas turbine engine including a unique pulse detonation combustion system. In some embodiments, the pulse detonation combustion system includes an inlet section, a vortex generator and at least one flame accelerator. The inlet section, vortex generator and the at least one flame accelerator may be operative to initiate a deflagration to detonation transition. In some embodiments, the pulse detonation combustion system may include a flame accelerator configured with a directionally-dependent drag coefficient. Other embodiments include apparatuses, systems, devices, hardware, methods, and combinations for pulse detonation combustion systems, gas turbine engines, and other machines and engines. Further embodiments, forms, features, aspects, benefits, and advantages of the present application shall become apparent from the description and figures provided herewith.