Hopf bifurcation control in a congestion control model via dynamic delayed feedback

Area of Science:

• Control Theory
• Network Engineering
• Dynamical Systems

Background:

• Bifurcation control aims to prevent or delay unwanted dynamic system changes.
• Hopf bifurcations are critical in understanding system stability, particularly in congestion control models.
• Existing methods may not adequately address Hopf bifurcations in second-order systems with delays.

Purpose of the Study:

• To design and implement a dynamic delayed feedback controller for Hopf bifurcation control.
• To enhance the critical communication delay in a second-order congestion control model.
• To ensure a stationary data sending rate for systems experiencing larger delays.

Main Methods:

• Development of a dynamic delayed feedback controller.
• Application of a perturbation approach to derive analytical formulas.
• Numerical simulations to validate controller performance.

Main Results:

• The developed controller successfully creates Hopf bifurcations at desired locations.
• A significant increase in the critical communication delay was achieved.
• Explicit formulas for the period and direction of bifurcating periodic solutions were derived.
• Numerical simulations confirmed the controller's efficacy.

Conclusions:

• The dynamic delayed feedback controller is an effective tool for managing Hopf bifurcations in congestion control.
• The controller enhances system stability by increasing the tolerance to communication delays.
• This approach offers a method to guarantee stable data transmission rates in dynamic networks.