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

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

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

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.

Keywords: Demand-supply model; Line demand; Non-line demand; Inventory; Ordinary differential equations (search for similar items in EconPapers)
Date: 2026
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925014419
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925014419

DOI: 10.1016/j.chaos.2025.117428

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().