Tipping points, multistability, and stochasticity in a two-dimensional traffic network dynamics

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Urban Transportation

Background:

• Urban transportation networks are intricate systems prone to traffic congestion.
• Mitigating traffic jams is crucial for improving urban mobility and efficiency.

Purpose of the Study:

• To investigate the dynamics of vehicular traffic flow in a macroscopic two-dimensional network model.
• To analyze the impact of parameters like occupancy, entry, and exit rates on traffic flow.
• To explore phenomena such as multistability, stochastic switching, and critical transitions.

Main Methods:

• Utilized nonlinear dynamics techniques to model vehicular traffic flow.
• Employed single and biparametric bifurcation diagrams to identify various bifurcation types.
• Applied basin stability metrics to quantify multistability and analyzed critical slowing down indicators.

Main Results:

• Identified saddle-node, Hopf, homoclinic, Bogdanov-Takens, and cusp bifurcations in the traffic network.
• Characterized multistability, stochastic switching, and critical transitions from free flow to congestion.
• Demonstrated that traffic congestion is caused by either bifurcation or stochasticity.

Conclusions:

• Traffic congestion in urban networks is driven by underlying system bifurcations or random fluctuations.
• The study provides insights into the tipping mechanisms of traffic jams.
• Findings can inform strategies for managing and mitigating urban traffic congestion.