Hysteresis phenomenon of mode transition in ramjet engines and its topological rule

A mechanical model is developed in line with the principles of bistability in dynamical system theories for investigating the nonlinear behavior of mode transition under the assumption of inviscid flow. The hysteresis phenomenon of mode transition in a ramjet engine is identified in an analytical way. It is found through mechanical analysis that the hysteresis phenomenon originates from the unstable positive feedback mechanism of shock motion in the converging channel of Laval nozzle. The hysteresis phenomenon disappears once the unstable positive feedback mechanism is removed by replacing the converging channel with a constant area channel. The topological rule that governs the hysteresis phenomenon of mode transition in a ramjet engine is also discovered using Thom's classification theorem in dynamical system theories.