Abstract
In this paper, we address the problem of the bifurcation control of a delayed fractional-order dual model of congestion control algorithms. A fractional-order proportional-derivative (PD) feedback controller is designed to control the bifurcation generated by the delayed fractional-order congestion control model. By choosing the communication delay as the bifurcation parameter, the issues of the stability and bifurcations for the controlled fractional-order model are studied. Applying the stability theorem of fractional-order systems, we obtain some conditions for the stability of the equilibrium and the Hopf bifurcation. Additionally, the critical value of time delay is figured out, where a Hopf bifurcation occurs and a family of oscillations bifurcate from the equilibrium. It is also shown that the onset of the bifurcation can be postponed or advanced by selecting proper control parameters in the fractional-order PD controller. Finally, numerical simulations are given to validate the main results and the effectiveness of the control strategy.
| Original language | English |
|---|---|
| Pages (from-to) | 2185-2198 |
| Number of pages | 14 |
| Journal | Nonlinear Dynamics |
| Volume | 90 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Nov 2017 |
Bibliographical note
Publisher Copyright:© 2017, Springer Science+Business Media B.V.
Keywords
- Hopf bifurcation
- algebra
- bifurcation theory
- stability and control
- time delay systems