The invention discloses a pulse oscillation device constructed and designed based on a mathematical model, and relates to the technical field of pulse oscillators. The pulse oscillation device comprises a shell, a jet flow inlet, a first discrete vortex, a jet flow outlet, a second discrete vortex, a first air steam bag, a second air steam bag, first air bubbles and second air bubbles, and the jetflow inlet is fixedly formed in the top of the shell. According to the pulse oscillation device constructed and designed based on the mathematical model, the jet flow impact performance is high, thepulse signal mutability is high, the amplitude change is stable, the improvement on jet flow impact performance is facilitated, the characteristic of the stable pulse effect is achieved, an internal system is stable, large-scale vortexes existing in an oscillation cavity and the pulse pressure oscillation effect can cause vortex cavitation and oscillation cavitation formation in a self-oscillationcavity, and therefore the cavitation effect of the jet flow outlet is enhanced, the cavitation effect of the jet flow is effectively promoted, meanwhile, transmission and superposition of water pressure signals are facilitated, and the cracking problem is not prone to occurring.