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Mathematical Problems in Engineering
Volume 2016, Article ID 2706719, 15 pages
Research Article

Stability and Hopf Bifurcation Analysis on a Nonlinear Business Cycle Model

Department of Management and Economics, Tianjin University, Tianjin 300072, China

Received 27 February 2016; Revised 5 June 2016; Accepted 11 July 2016

Academic Editor: Sergey A. Suslov

Copyright © 2016 Liming Zhao and Zhipei Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study begins with the establishment of a three-dimension business cycle model based on the condition of a fixed exchange rate. Using the established model, the reported study proceeds to describe and discuss the existence of the equilibrium and stability of the economic system near the equilibrium point as a function of the speed of market regulation and the degree of capital liquidity and a stable region is defined. In addition, the condition of Hopf bifurcation is discussed and the stability of a periodic solution, which is generated by the Hopf bifurcation and the direction of the Hopf bifurcation, is provided. Finally, a numerical simulation is provided to confirm the theoretical results. This study plays an important role in theoretical understanding of business cycle models and it is crucial for decision makers in formulating macroeconomic policies as detailed in the conclusions of this report.