A Dynamic Competition Analysis on the Personal Computer Shipments in Taiwan Using Lotka-Volterra Model

Abstract

In this work, we explore the innovative growth of personal computer (PC) shipments in Taiwan. We estimate the marketing diffusion with the consideration of the competition of desktop (DT) and notebook (NB). Mathematically, using the Lotka-Volterra model, we analyze the dynamic competitive relationship between the shipments of DT and NB. All the parameters in the Lotka-Volterra model are calibrated with the realistic shipment data, and the predicted trends to 2010 are thus drawn. Our results clarify a pure competition between DT and NB in PC market. The competitive relationship of dynamic PC shipments in Taiwan is thus examined, including consideration of the interaction between two species to explain the actual diffusion phenomenon in the competitive market. Comparison between well-known growth model, Bass model, and competitive Lotka-Volterra Model is also drawn. In addition, it is shown that the competition between DT and NB would reach an equilibrium point which is stable over time and we further analyze how the deviation returns to the stable equilibrium.

Ecosystem Stability Analysis and Numerical Simulation via Three Improved Lotka-Volterra Models

“…Ma et al used the LV model to perform voltage stability analysis of power systems based on bifurcation theory [15]. Chiang et al discussed the innovative growth of Taiwan's personal computer (PC) shipments, analyzing the dynamic competitive relationship between PC categories using the LV model to explain the actual diffusion phenomenon in the competitive market [16]. Luo et al studied the collinear competition between urban rail and bus public transport based on the population competition model.…”