Calculating (transient) rate of cycles of practical thermodynamic engines (turbojet, multi-cylinder car engines etc..)

I tried to make a plan for a turbojet engine with my physics knowledge and I’m stumped in the first step. For any sustained real engine, I need to somehow take a fraction of the energy output and use that to drive the engine into the next cycle. Take carnot cycle for example. For an engine based on that cycle, I need to take part of the total energy output in one cycle and use that to supply the work done in the cold isotherm in next cycle. Or we could use two out of phase carnot cycles and somehow couple them together and depending on how we actually build the engines, there will be some physics that will determine the equilibrium frequency of the engine(cycles per second). I can’t seem to find out what the actual physics is in the case of gas turbine engines. All I found after doing google search are the phrases "compressor-turbine matching" and "compressor turbine operating line" with no solid physics whatsoever. However, it is clear that you increase the cycle rate by increasing fuel injection rate so it must be a function of that. But how do I calculate the rate of cycles(here turbine rpm will do) in this case?