Stability and Hopf Bifurcation of a Four-Dimensional Dynamic Economic System

Hong-liang Tu () and Jun-hai Ma ()
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Hong-liang Tu: Tianjin University
Jun-hai Ma: Tianjin University

Chapter Chapter 57 in The 19th International Conference on Industrial Engineering and Engineering Management, 2013, pp 599-611 from Springer

Abstract: Abstract In this paper, first of all, a four-dimensional dynamic economic system is established. First, choosing the saving rate as the bifurcation parameter, the stability and Hopf bifurcation of the system are studied. Then, a example of simulation of the model is used to prove the derived results in Sect57.2. Furthermore, a time-delayed feedback is added to the dynamic finance system. Choosing the delay as the bifurcation parameter, the local stability and the existence of Hopf bifurcation of the model with delay are researched. Stability changes and Hopf bifurcation happens while the delay passes through a critical value. We can see that increasing the delay can lead the dynamic economic system to fluctuate. Then, a numerical example is taken to confirm the theoretical results obtained in Sect.57.3. Finally, some conclusions are made. This paper has an important theoretical and practical significance.

Keywords: Dynamic economic system; Hopf bifurcation; Stability; Time delay; Time-delayed feedback (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-37270-4_57

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DOI: 10.1007/978-3-642-37270-4_57

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