Hopf Bifurcation and Stability Analysis of a Business Cycle Model With Time-Delayed Feedback
|International Journal of Engineering Trends and Technology (IJETT)||
|© 2018 by IJETT Journal|
|Year of Publication : 2018|
|Authors : Lei Peng, Yanhui Zhai
|DOI : 10.14445/22315381/IJETT-V61P223|
MLA Style: Lei Peng, Yanhui Zhai "Hopf Bifurcation and Stability Analysis of a Business Cycle Model With Time-Delayed Feedback" International Journal of Engineering Trends and Technology 61.3 (2018): 138-148.
APA Style:Lei Peng, Yanhui Zhai, (2018). Hopf Bifurcation and Stability Analysis of a Business Cycle Model With Time-Delayed Feedback. International Journal of Engineering Trends and Technology, 61(3), 138-148.
In this paper, a business cycle model with time-delayed feedback is investigated. Firstly, we add a time-delayed feedback controller to the business cycle model and propose a new model. Secondly, the linear stability of the model and the local Hopf bifurcation are studied and we derive the conditions for the stability and the existence of Hopf bifurcation at the equilibrium of the system. Besides, the direction of Hopf bifurcation and the stability of bifurcation periodic solutions are studied by adopting the center manifold theorem and the normal form theory. At last, some numerical simulation results are presented to confirm that the controller can effectively increase the stability region of the business cycle model.
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Business cycle model,Time-delayed feedback, Stability, Hopf bifurcation, Numerical simulation.