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On The Hopf Bifurcation And Equilibrium Points Of Partial Benefit Symbiosis Of Financial Market Using Delay Differential Equations

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  • DONGSHENG LI

    (School of Economics and Finance, Chongqing University of Technology, Chongqing 400054, P. R. China)

  • DIPESH

    (��Department of Mathematics, SR University, Warangal, Telangana 506371, India)

  • SIBEL PAÅžALI ATMACA

    (��Department of Mathematics, Faculty of Science, Mugla Sıtkı Koçman University, Muğla, Turkey)

  • PANKAJ KUMAR

    (�Department of Mathematics, Lovely Professional University, Phagwara, Punjab 144411, India)

Abstract

The financial market’s behavior is complex and nonlinear, characterized by chaos rather than simplicity and linearity. Numerous factors contribute to this complex behavior, which many traditional forecasting models fail to account for. This proposed model incorporates the concept of partial benefit symbiosis, where one party gains significantly through funds provided by banks without negatively impacting other parties. This results in a delayed profit share for the other parties, represented by a delay parameter. The companies’ growth is modeled using a logistic function, and the stability of the system is examined around a positive market equilibrium. Analytical results are supported by MATLAB simulations. This comprehensive analysis not only enhances conceptual understanding but also improves market forecasting, contributing to sustained economic growth and development.

Suggested Citation

  • Dongsheng Li & Dipesh & Sibel Paåžali Atmaca & Pankaj Kumar, 2025. "On The Hopf Bifurcation And Equilibrium Points Of Partial Benefit Symbiosis Of Financial Market Using Delay Differential Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(08), pages 1-9.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:08:n:s0218348x25401607
    DOI: 10.1142/S0218348X25401607
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