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Complete Stability Analysis for Delayed Economic Systems

Author

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  • Jun-Xiu Chen

    (Department of Basic Courses Teaching, Dalian Polytechnic University, Dalian 116034, China)

  • Gao-Xia Fan

    (State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
    School of Information Science and Engineering, Northeastern University, Shenyang 110819, China)

  • Xu Li

    (School of Modern Posts, Nanjing University of Posts and Telecommunications, Nanjing 210003, China)

Abstract

In this paper, we will study the stability of economic systems with delay, also called delayed economic systems. We focus on the complete stability problem with respect to delay for linearized economic systems. First, we will review three types of delayed economic systems and will see that the characteristic functions are all in the form f ( λ , τ ) . Then, we will solve the complete stability problem by using the frequency-sweeping approach, which is introduced for the stability studies of economic systems (for the first time). As a consequence, the complete stability problem with delayed economic systems can be systematically solved. Finally, numerical examples will show that the whole stability set of τ for a delayed economic system may be determined accurately.

Suggested Citation

  • Jun-Xiu Chen & Gao-Xia Fan & Xu Li, 2025. "Complete Stability Analysis for Delayed Economic Systems," Mathematics, MDPI, vol. 13(13), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2112-:d:1689400
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    References listed on IDEAS

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    3. Krawiec, Adam & Szydłowski, Marek, 2017. "Economic growth cycles driven by investment delay," Economic Modelling, Elsevier, vol. 67(C), pages 175-183.
    4. Torre, V, 1977. "Existence of Limit Cycles and Control in Complete Keynesian System by Theory of Bifurcations," Econometrica, Econometric Society, vol. 45(6), pages 1457-1466, September.
    5. A. Krawiec & M. Szydlowski, 1999. "The Kaldor‐Kalecki business cycle model," Annals of Operations Research, Springer, vol. 89(0), pages 89-100, January.
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