Hopf Bifurcation Control Based on a Stochastic Traffic Flow Model

The study of stochastic behavior in traffic flow is crucial for uncovering its intrinsic evolutionary mechanisms and optimizing traffic management. This paper extends the optimal velocity-relative velocity (OVRV) model by introducing a stochastic function, aiming to investigate Hopf bifurcation phenomena and their control strategies in stochastic traffic flow. Via systematic theoretical deductions, this study verifies the occurrence of Hopf bifurcation at the system’s equilibrium states, and develops two types of feedback controllers—linear and stochastic nonlinear ones—to adjust the bifurcation threshold and suppress the amplitude of limit cycles. Numerical simulations demonstrate that tuning controller parameters can effectively postpone or eliminate Hopf bifurcations while drastically mitigating limit cycle amplitudes. Furthermore, the theoretical model’s applicability is validated using empirical data from a real traffic scenario. Research findings indicate that when traffic density approaches the Hopf bifurcation critical value, the roadway exhibits congestion characterized by constant-amplitude oscillations; after implementing feedback control, density fluctuations are significantly reduced and system stability is restored. This research establishes a stochastic bifurcation control framework for traffic flow, offering theoretical guidance for active congestion management and laying a foundation for cooperative control in connected and autonomous vehicle scenarios.