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Dynamics of a stockless market through piecewise smooth models

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  • Molina-Díaz, Oscar Emilio
  • Olivar-Tost, Gerard
  • Sotelo-Castelblanco, Deissy Milena

Abstract

Markets play a crucial role in the economic activity of any country, serving as fundamental drivers of growth, development, and employment. Given their significance, understanding the dynamics of markets is essential. In this study, we present a mathematical model to characterize the behavior of a stockless market. The model is formulated using a system of ordinary differential equations defined with piecewise smooth functions. We conduct a mathematical analysis of the model, particularly focusing on the behavior of trajectories as they approach switching surfaces using Filippov’s analysis. Furthermore, we provide numerical simulations to visually illustrate the model’s dynamics and a insights a brief study of bifurcations is done.

Suggested Citation

  • Molina-Díaz, Oscar Emilio & Olivar-Tost, Gerard & Sotelo-Castelblanco, Deissy Milena, 2024. "Dynamics of a stockless market through piecewise smooth models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 246-269.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:246-269
    DOI: 10.1016/j.matcom.2024.07.009
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    References listed on IDEAS

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    6. 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.
    7. Lin, Chiun-Sin, 2013. "Forecasting and analyzing the competitive diffusion of mobile cellular broadband and fixed broadband in Taiwan with limited historical data," Economic Modelling, Elsevier, vol. 35(C), pages 207-213.
    8. Modis, Theodore, 1999. "Technological Forecasting at the Stock Market," OSF Preprints ctd6s_v1, Center for Open Science.
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    Cited by:

    1. Oscar Emilio Molina-Díaz & Gerard Olivar-Tost & Deissy Milena Sotelo-Castelblanco, 2024. "Fold-Fold Singularity in a Piecewise Smooth Mathematical Model Describing the Dynamics of a Stockless Market," Mathematics, MDPI, vol. 12(16), pages 1-18, August.

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