In this work, we for the first time study the inter-industrial clustering behaviors of integrated circuit (IC) industry from Taiwan to China via amount of foreign direct investment (FDI). According to the mutual dependence among IC design, manufacturing and packaging-and-testing industries, Lotka-Volterra model is solved to explore the cluster evolutions. Effects of inter-level collaborations along production value chain on FDI flows into China are considered. Evolution of FDI into China for IC design industry significantly inspires the subsequent FDI of IC manufacturing, packaging and testing industries. Since the production of IC manufacturing, packing and testing enterprises depends on the preceded products that design industry has devised, the middle-stream manufacturing and downstream packaging-and-testing firms tend to converge toward upstream design houses. Taiwan IC industry's FDI amount into China is estimated to be cumulatively increasing, which suggests the clustering tendency of Taiwan IC industry. Prediction of FDI with Lotka-Volterra model is superior to that of the conventional growth model (i.e., Bass model) because the industrial mutualism among various stages is included. The flows of FDI have not yet reached equilibrium points, so the FDI inflows into China will expand for IC design or packaging-and-testing industry, while decline for manufacturing industry.