A supersonic propulsion system is provided. The supersonic propulsion system includes a plurality of systems for efficiently creating cyclic detonations and at least one rocket booster device. Each of the systems include at least a first initiator chamber configured to generate an initial wave, at least one main chamber coupled to the first initiator chamber. The main chamber is configured to generate a main wave and to output products of supersonic combustion. The products are generated within the main chamber. The main chamber is configured to enable the main wave to travel upstream and downstream within the main chamber when the first initiator chamber is located outside the main chamber. The system further includes an initial connection section located between the first initiator chamber and the main chamber that enhances a combustion process via shock focusing and shock reflection.