This study started from the perspective of predicting science and technology competition, building on this to discuss the dynamic competition between Android and iOS by sales volume in each quarter. The Lotka-Volterra system of equations, one well-known competitive diffusion models, has been adopted to represent the competitive situations of the smartphone operating system market, with the Lyapunov function used to carry out equilibrium and stability analysis. The results showed that Android and iOS have a predator-prey relationship, in which iOS serves as the predator, and Android as a prey. The equilibrium and stability analysis show that both products are able to coexist in the market, and thus, each system has its own stable sales volume.