Unveiling critical transition in a transport network model: stochasticity and early warning signals - Chattopadhyay, Shankha Narayan; Gupta, Arvind Kumar (Nonlinear dynamics, 2025)
Abrupt shifts between stable states frequently occur in complex systems, from natural phenomena like ecosystem collapse to engineered systems namely traffic flow. These transitions, which can be sudden and severe, are anticipated using statistical tools or early warning signals (EWSs), valued for their broad applicability. This study examines a two-dimensional autonomous vehicular traffic flow model and extends it with a stochastic version using a multiplicative Gaussian process. PRCC analysis is conducted to gain an in-depth understanding of the model’s robustness and assess how variations in different parameter configurations affect the results. Detailed bifurcation analysis reveals important characteristics of the deterministic model, including bistability, tristability, and tetrastability. Phase portraits and basin stability measures further investigate these bifurcation results. It is revealed that transitions between low-density and high-density traffic regimes can occur due to saddle-node bifurcations and noise. Two-parameter diagrams pinpoint specific domains where the system achieves unique or multiple equilibrium points, illustrating how parameters influence the number of steady states. The confidence ellipse method identifies threshold noise levels signalling a shift between attractors. EWSs are utilised to predict regime shifts caused by bifurcation-induced and noise-driven transitions. In the former, variance serves as a strong predictor, effectively detecting critical shifts due to changes in exit rates, while lag-1 autocorrelation proves less reliable. In the stochastic switching context, lag-1 autocorrelation performs marginally better than variance. Additionally, conditional heteroskedasticity is also employed to detect B-tipping and N-tipping points prior. However, its performance gets hampered while anticipating the second instance. These findings suggest that EWSs can effectively predict critical traffic transitions if applied with caution. The study offers valuable insights for traffic management strategies to anticipate and alleviate congestion in urban networks.