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Some application of ordinary differential equations in several areas of the economy

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  • Xia, Hongmei
  • Yang, Meirong
  • Han, Guoxiang
  • Huang, Yuchuan
  • Fang, Yudong
  • Meng, Dongyue

Abstract

Market research typically relies on supply and demand curves, but studies analysing market stability using ordinary differential equations (ODEs) remain insufficient. This study presents a unified multidimensional ODE framework that integrates linear and nonlinear demand functions with inventory dynamics to systematically assess market equilibrium stability. Key findings include: Li et al. (2025) (1) linear demand models consistently produce stable equilibria; Sinha and Lucheroni (2024) (2) nonlinear demand functions can yield multiple outcomes, including two equilibria (one stable, one unstable), a single unstable point, or no equilibrium, depending on parameters and initial conditions; and (Shapiro, 2024 (3)) inventory effects lead to either gradual or oscillatory convergence to equilibrium. Bifurcation analysis shows that variations in the α parameter significantly affect equilibrium and stability, especially in nonlinear models with complex dynamics. MATLAB simulations visualize and validate the results, enhancing clarity and practical relevance. This research provides new insights into dynamic supply-demand interactions and establishes a solid theoretical foundation for future economic analysis.

Suggested Citation

  • Xia, Hongmei & Yang, Meirong & Han, Guoxiang & Huang, Yuchuan & Fang, Yudong & Meng, Dongyue, 2026. "Some application of ordinary differential equations in several areas of the economy," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925014419
    DOI: 10.1016/j.chaos.2025.117428
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    References listed on IDEAS

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    1. Qi Feng & J. George Shanthikumar, 2018. "Supply and Demand Functions in Inventory Models," Operations Research, INFORMS, vol. 66(1), pages 77-91, 1-2.
    2. Kilian, Lutz, 2022. "Understanding the estimation of oil demand and oil supply elasticities," Energy Economics, Elsevier, vol. 107(C).
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    4. Vladislav Gennadievich Malyshkin, 2016. "Market Dynamics. On Supply and Demand Concepts," Papers 1602.04423, arXiv.org.
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    7. David Baqaee & Emmanuel Farhi, 2022. "Supply and Demand in Disaggregated Keynesian Economies with an Application to the COVID-19 Crisis," American Economic Review, American Economic Association, vol. 112(5), pages 1397-1436, May.
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