1. Stability and Hopf bifurcation analysis of a TCP/RAQM network with ISMC procedure.
- Author
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Khoshnevisan, Ladan, Liu, Xinzhi, and Salmasi, Farzad R.
- Subjects
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HOPF bifurcations , *DELAY differential equations , *TCP/IP , *BIFURCATION theory , *ERROR rates - Abstract
Highlights • A network with wireless access links with a delay differential equation (DDE) model and input delay is considered. • Integral sliding mode control is assumed as the nonlinear robust active queue management in the network. • Hopf bifurcation analysis is investigated with the transmission delay considered as the Hopf bifurcation parameter. • The direction and the stability of the bifurcation periodic solutions are determined. • Simulation results are provided to illustrate the system behavior with different parameters. Abstract Transmission control protocol (TCP), which is usually implemented in the transport layer of a communication network, can detect the congestion after its occurrence. But congestion control can be more complicated in networks with wireless access links due to time-varying fading and packet error rate (PER). Thus, it is essential to use robust active queue management (RAQM) to prevent congestion with certain tolerance against serious disturbance of the wireless environment. As the stability of a TCP/RAQM is tremendously related to the transmission delay, this paper focuses on Hopf bifurcation analysis of a network governed by nonlinear delayed differential equations and an integral sliding mode control as a nonlinear RAQM. The transmission delay is assumed as the bifurcation parameter. It is shown that if the delay passes through a critical value, the closed loop system would not remain stable and the Hopf bifurcation occurs. Moreover, based on the normal form theory and the center manifold theorem, the direction and the stability of the bifurcation periodic solutions are determined. Finally, simulation results are given to confirm the analytical achievements and to show the effectiveness of the procedure compared to some recent protocols. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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