Nonlinear Dynamics

, Volume 76, Issue 1, pp 497–508 | Cite as

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

  • Junhai Ma
  • Hongliang Tu
Original Paper


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.


Stability Hopf bifurcation Dynamics Macro-economy system Delay 



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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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.College of Management and EconomicsTianjin UniversityTianjinChina
  2. 2.School of ManagementChina University of Mining and TechnologyXuzhouChina

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