延迟分数阶供应链金融模型的稳定性与Hopf分岔研究

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中图分类号：F832.0;F224 文献标识码：A 文章编号：1672-3791（2026）03-0242-04

Research on Stabilityand Hopf Bifurcation of Fractional-Order Supply Chain Finance Model with Time Delay

YANBinbin ZHANG Xingjing

School of Mathematics and Statistics，Guizhou Universityof Finance and Economics，Guiyang，Guizhou Provice， 550025 China

Abstract： Supply chain finance serves as an important approach to alleviate the financing difculties of smalland medium-sized enterprises.Most existing studies are basedon classical game theory methods，with lessconsideration givento the impact of time-delay effectsand long-memory characteristics on theevolutionof decisions.To reveal the complex dynamic behaviors of the supply chain finance system，a dynamic game model between banks and smallandmedium-sizedenterprises isconstructedinthisarticle.Byintroducing timedelayandfractional-orderderivatives，afractional-order game model with delayis established.Basedon the stability theoryoffractional-order diffrential equations and bifurcation principles，the critical threshold for the system to undergo Hopf bifurcation is derived. Finally，several suggestions for reducing time delays are proposed based on the simulation results.

Keywords： Supply chain finance; Fractional order; Game model; Time delay;Evolutionary stable strategy; Hopf bifurcation

供应链金融以核心企业信用为依托，整合产业链上下游资源，将中小企业的资产转化为融资凭证，缓解其融资约束。（剩余4253字）