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Analysis of the stability and Hopf bifurcation of money supply delay in complex macroeconomic models

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Abstract

Considering the macroeconomic model of money supply, this paper carries out the corresponding extension of the complex dynamics to macroeconomic model with time delays. By setting the parameters, we discuss the effect of delay variation on system stability and Hopf bifurcation. Results of analysis show that the stability of time-delay systems has important significance with the length of time delay. When time delay is short, the stable point of the system is still in a stable region; when time delay is long, the equilibrium point of the system will go into chaos, and the Hopf bifurcation will appear in certain conditions. In this paper, using the normal form theory and center manifold theorem, the periodic solutions of the system are obtained, and the related numerical analysis are also given; this paper has important innovation-theoretical value and acts as important actual application in macroeconomic system.

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Acknowledgements

This work was supported by The National Nature Science Foundation of China (grant No. 61273231) and supported by Doctoral Fund of Ministry of Education of China (grant No. 20130032110073).

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Authors and Affiliations

  1. College of Management and Economics, Tianjin University, Tianjin, 300072, China

    Junhai Ma & Hongliang Tu

  2. School of Management, China University of Mining and Technology, Xuzhou, 221116, China

    Hongliang Tu

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  1. Junhai Ma
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  2. Hongliang Tu
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Correspondence to Junhai Ma or Hongliang Tu.

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Ma, J., Tu, H. Analysis of the stability and Hopf bifurcation of money supply delay in complex macroeconomic models. Nonlinear Dyn 76, 497–508 (2014). https://doi.org/10.1007/s11071-013-1143-x

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  • DOI: https://doi.org/10.1007/s11071-013-1143-x

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