Worked with my girlfriend as a research project as a means to learn more about this experimental engine 

A rotating detonation engine unlike most other engines whose combustion is a deflagration works on the principle of rotating detonation waves travelling at mach 5+ speeds. They work on the Humphry cycle and are theoretically 25% more efficient than in comparison to the Brayton cycle. With the Humphry cycle being a constant volume process it is able to extract more work. Efficiency is further improved by not needed a compressor as the detonation wave itself is able to compress and ignite the new fuel and air mixture. Reading the literature we found that the detnoation is modelled using the Chapman-jouget  mathematical model and the more refined ZND model for detonation yielding very high pressure ratios. We worked out the equations found in those papers for our design as well

Due to the process being so violent with temperatures exceeding material limits this posses the need for regenerative cooling methods. Reading multiple literature works we see many problems are yet to be solved before RDE's are adopted widely. Researchers still have no 100% reliable method of starting a detonation wave inside the chamber, works from china have found success in adopting a pre detonation inlet feeding into the main chamber as a reliable means. There also existing the problem of backflow into the injector due to the high pressure and developing more efficient mixing for the fuel and oxidiser between detonation waves. 

All these are not unsolvable problems and in addition with an aerospike the Rotating detonation engine is on paper is superior in terms of part number complexity, efficiency and operating ranges for speed and altitude. 

Where turbojets, rocket engines, scramjets etc. Operate best at specific conditions.