Chaotic dynamics in the software market with network externalities

In this study, we built discrete-time dynamic systems to investigate the chaotic dynamics of a software market with network externalities. Monopoly and duopoly systems are considered separately. The chaotic features of both monopoly and duopoly models are verified through numerical simulations, including bifurcation diagrams, maximal Lyapunov exponent, and strange attractors. In the monopoly model, the strategy of distributing low-quality versions is evaluated. The impacts of decision parameters on the dynamics of the system are also investigated. Meanwhile, the Ott, Grebogi, and Yorke method is adopted to control chaos in the monopoly model by making moderate changes in the market evolution speed of the low-quality version software. In the duopoly model, the system dynamics are illustrated numerically. Three different cases are considered in evaluating decisions of firms regarding distribution or non-distribution of the low-quality version software. Furthermore, the compatibility parameter is examined with regards to its impacts on the dynamics of the duopoly system.