Hopf Bifurcation and Stability Analysis in a Price Model with Time-Delayed Feedback

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2018 by IJMTT Journal
Volume-62 Number-1
Year of Publication : 2018
Authors : Lei Peng, Yanhui Zhai
  10.14445/22315373/IJMTT-V62P509

MLA

MLA Style: Lei Peng, Yanhui Zhai "Hopf Bifurcation and Stability Analysis in a Price Model with Time-Delayed Feedback" International Journal of Mathematics Trends and Technology 62.1 (2018): 55-66.

APA Style: Lei Peng, Yanhui Zhai (2018). Hopf Bifurcation and Stability Analysis in a Price Model with Time-Delayed Feedback. International Journal of Mathematics Trends and Technology, 62(1), 55-66.

Abstract
A Rayleigh price model with time-delayed feedback is investigated in this paper. First, a time-delayed feedback controller is introduced to the Rayleigh price model and we discussed the effect of the delay on the system. Second, the linear stability of the model and the local Hopf bifurcation are studied and we derived 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 confirmed that the feasibility of the theoretical analysis.

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Keywords
Rayleigh price model,Time-delayed, Hopf bifurcation, Stability, Numerical simulation.