Stability and Hopf Bifurcation of Simplified Fluid Flow Model for Wireless Network with PD Control

Na Han; Yanhui Zhai

doi:https://doi.org/10.14445/22315373/IJMTT-V66I12P514

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 12 | Year 2020 | Article Id. IJMTT-V66I12P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I12P514

Stability and Hopf Bifurcation of Simplified Fluid Flow Model for Wireless Network with PD Control

Na Han, Yanhui Zhai

Citation :

Na Han, Yanhui Zhai, "Stability and Hopf Bifurcation of Simplified Fluid Flow Model for Wireless Network with PD Control," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 12, pp. 91-105, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I12P514

Abstract

In this paper, based on the control and bifurcation theory, a PD controller is proposed to control the Hopf bifurcation of the fluid flow model in the wireless network congestion control stystem. First, communication delay is selected as a bifurcation parameter to obtain the critical value of communication delay that keeps the original system and the conrolled system stable. When the delay value exceeds the critical value, the system will lose stability at the equilibrium point and generate Hopf bifurcation. It is found that the addition of PD controller can effectively delay the generation of Hopf bifurcation, increase the critical value of bifurcation parameters, and expand the stability region. Besides, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by using the center manifold theorem and the normal form theory. At last, some numerical simulation results with mathematical software are confirmed that the feasibility of the theoretical analysis.

Keywords

Center manifold theorem, Hopf bifurcation, Normal form theory, PD controller, Stability

References

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