Hybrid control dynamic model analysis of Hopf bifurcation for fractional order congestion control systems with time delay

This paper introduces a novel hybrid control strategy integrating state feedback and parameter perturbation to analyze the Hopf bifurcation dynamics in fractional-order congestion control systems. Initially, we examine the system’s characteristic equation using time delay as the bifurcation parameter, establishing stability conditions and Hopf bifurcation criteria under hybrid control. Our findings reveal that when communication delay surpasses a critical threshold, the system undergoes Hopf bifurcation. Subsequently, we demonstrate how to postpone this bifurcation by fine-tuning control parameters while preserving the system’s equilibrium point. Numerical simulations validate our theoretical framework, effectively mapping the system’s stability boundaries. The results provide practical insights for optimizing network congestion control mechanisms. Both analytical models and computational simulations confirm that this approach successfully postpones bifurcation onset. Consequently, it broadens the stable operational range within parameter space and enhances congestion control system performance a finding with substantial real-world applications. Additionally, our research reveals that fractional order and interaction coefficients significantly influence network dynamics. System stability notably increases as these parameters diminish.