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<p>Various traffic phenomena, such as traffic congestion, stop-and-go waves, and shock waves, often occur alternately in traffic systems. The essence of these abrupt changes lies in bifurcation behaviors triggered by different causes in traffic flow. When the traffic system passes through certain critical bifurcation points, the qualitative state of the system changes suddenly, leading to traffic instability. Based on a macroscopic traffic flow model that incorporates driver reaction effects, this paper employs bifurcation theory in nonlinear dynamics to analyze traffic congestion and stability transitions caused by bifurcations in traffic systems. First, the linear stability region of the macroscopic model is derived using linear stability theory. Second, bifurcation analysis is conducted on the macroscopic model to determine the conditions for the existence of Hopf bifurcations, identify stability changes in the traffic system, and analyze the relationship between stability transitions and bifurcation points. Finally, for unstable bifurcation points, a feedback controller is designed using nonlinear feedback control methods. By regulating the amplitude of the Hopf bifurcation limit cycle, the onset of the Hopf bifurcation is delayed, thereby alleviating traffic congestion.</p>

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Hopf bifurcation analysis and control of traffic flow models considering driver reaction effects

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Wenhuan Ai,
  • Dongqiang Su,
  • Shaokang Wang,
  • Xiaoyi Shi,
  • Lingyi Ouyang

摘要

Various traffic phenomena, such as traffic congestion, stop-and-go waves, and shock waves, often occur alternately in traffic systems. The essence of these abrupt changes lies in bifurcation behaviors triggered by different causes in traffic flow. When the traffic system passes through certain critical bifurcation points, the qualitative state of the system changes suddenly, leading to traffic instability. Based on a macroscopic traffic flow model that incorporates driver reaction effects, this paper employs bifurcation theory in nonlinear dynamics to analyze traffic congestion and stability transitions caused by bifurcations in traffic systems. First, the linear stability region of the macroscopic model is derived using linear stability theory. Second, bifurcation analysis is conducted on the macroscopic model to determine the conditions for the existence of Hopf bifurcations, identify stability changes in the traffic system, and analyze the relationship between stability transitions and bifurcation points. Finally, for unstable bifurcation points, a feedback controller is designed using nonlinear feedback control methods. By regulating the amplitude of the Hopf bifurcation limit cycle, the onset of the Hopf bifurcation is delayed, thereby alleviating traffic congestion.