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

Lei Peng; Yanhui Zhai

doi:https://doi.org/10.14445/22315373/IJMTT-V62P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 62 | Number 1 | Year 2018 | Article Id. IJMTT-V62P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V62P509

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

Lei Peng, Yanhui Zhai

Citation :

Lei Peng, Yanhui Zhai, "Hopf Bifurcation and Stability Analysis in a Price Model with Time-Delayed Feedback," International Journal of Mathematics Trends and Technology (IJMTT), vol. 62, no. 1, pp. 55-66, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V62P509

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.

Keywords

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

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