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

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  • Chiang, Su-Yun

Abstract

In this paper, we explore the innovation growth of 200mm and 300mm silicon wafers from Taiwan. Using the historic data, we simulate the growth of the area of 200mm and 300mm 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 200mm silicon wafers and 300mm 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 200mm silicon wafers and 300mm 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 200mm silicon wafers and 300mm silicon wafers. The prey 200mm generation does not disappear completely; it finally settles to a constant market alongside the predator 300mm generation.

Suggested Citation

  • Chiang, Su-Yun, 2012. "An application of Lotka–Volterra model to Taiwan's transition from 200mm to 300mm silicon wafers," Technological Forecasting and Social Change, Elsevier, vol. 79(2), pages 383-392.
    • Handle: RePEc:eee:tefoso:v:79:y:2012:i:2:p:383-392
    DOI: 10.1016/j.techfore.2011.05.007
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    Cited by:

    1. Addolorata Marasco & Alessandro Romano, 2018. "Deterministic modeling in scenario forecasting: estimating the effects of two public policies on intergenerational conflict," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(5), pages 2345-2371, September.
    2. Yang, Chunyu & Huang, Jue & Lin, Zhibin & Zhang, Danxia & Zhu, Ying & Xu, Xinghua & Chen, Mei, 2018. "Evaluating the symbiosis status of tourist towns: The case of Guizhou Province, China," Annals of Tourism Research, Elsevier, vol. 72(C), pages 109-125.
    3. Marasco, A. & Picucci, A. & Romano, A., 2016. "Market share dynamics using Lotka–Volterra models," Technological Forecasting and Social Change, Elsevier, vol. 105(C), pages 49-62.
    4. Goran Dominioni & Addolorata Marasco & Alessandro Romano, 2018. "A mathematical approach to study and forecast racial groups interactions: deterministic modeling and scenario method," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1929-1956, July.
    5. Duan, Hong-Bo & Zhu, Lei & Fan, Ying, 2014. "A cross-country study on the relationship between diffusion of wind and photovoltaic solar technology," Technological Forecasting and Social Change, Elsevier, vol. 83(C), pages 156-169.
    6. Xiaoxia Fu & Ping Zhang & Juzhi Zhang, 2017. "Forecasting and Analyzing Internet Users of China with Lotka–Volterra Model," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-18, February.

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