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Volume 13
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Article

Complete Stability Analysis for Delayed Economic Systems

by
Jun-Xiu Chen
1,
Gao-Xia Fan
2,3,* and
Xu Li
4
1
Department of Basic Courses Teaching, Dalian Polytechnic University, Dalian 116034, China
2
State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
3
School of Information Science and Engineering, Northeastern University, Shenyang 110819, China
4
School of Modern Posts, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(13), 2112; https://doi.org/10.3390/math13132112 (registering DOI)
Submission received: 23 May 2025 / Revised: 20 June 2025 / Accepted: 26 June 2025 / Published: 27 June 2025
(This article belongs to the Special Issue Latest Advances in Mathematical Economics)
Versions Notes

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.
Keywords: complete stability analysis; frequency-sweeping approach; economic systems; stability; time delay complete stability analysis; frequency-sweeping approach; economic systems; stability; time delay

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MDPI and ACS Style

Chen, J.-X.; Fan, G.-X.; Li, X. Complete Stability Analysis for Delayed Economic Systems. Mathematics 2025, 13, 2112. https://doi.org/10.3390/math13132112

AMA Style

Chen J-X, Fan G-X, Li X. Complete Stability Analysis for Delayed Economic Systems. Mathematics. 2025; 13(13):2112. https://doi.org/10.3390/math13132112

Chicago/Turabian Style

Chen, Jun-Xiu, Gao-Xia Fan, and Xu Li. 2025. "Complete Stability Analysis for Delayed Economic Systems" Mathematics 13, no. 13: 2112. https://doi.org/10.3390/math13132112

APA Style

Chen, J.-X., Fan, G.-X., & Li, X. (2025). Complete Stability Analysis for Delayed Economic Systems. Mathematics, 13(13), 2112. https://doi.org/10.3390/math13132112

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