An application of Lotka–Volterra model to Taiwan's transition from 200 mm to 300 mm silicon wafers

In this paper, we explore the innovation growth of 200 mm and 300 mm silicon wafers from Taiwan. Using the historic data, we simulate the growth of the area of 200 mm and 300 mm silicon wafers manufactured in Taiwan by the competitive Lotka–Volterra model. The parameters in the Lotka–Volterra model estimated with the realistic data are obtained numerically. The dynamic growth of competitive relationship between 200 mm silicon wafers and 300 mm silicon wafers is then analyzed. To prove the performance of the model, we further compare the famous Bass model and the Lotka–Volterra model. We also perform the equilibrium analysis to determine the long-term stability state in the simulation trajectory. Our research exhibits that 200 mm silicon wafers and 300 mm silicon wafers show a prey–predator relationship under the assumption of natural competition in the global semiconductor market. From a managerial perspective, the coefficients in the Lotka–Volterra model of exponential growth, self-interaction and cross-interaction represent the strength of product attractiveness, niche capacity and interaction for two competition products. We also find that there exists a stable equilibrium state for 200 mm silicon wafers and 300 mm silicon wafers. The prey 200 mm generation does not disappear completely; it finally settles to a constant market alongside the predator 300 mm generation.

Research highlights
► A prey–predator relationship exists between 200 mm silicon wafers and 300 mm silicon wafers via the Lotka–Volterra model.
► Comparing Bass with Lotka-Volterra model, the latter is more appropriate to describe the competition in the semiconductor market.
► Transition to the 300 mm generation apparently has cost and technology advantage.
► Finally, 200 mm and 300 mm silicon wafers reach an equilibrium state.