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Density-dependent overtaking and its impact on chaotic jam and phase transitions in a two-lane lattice model on curved roads

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  • Tian, Chuan
  • Kang, Yi-rong

Abstract

Density-dependent overtaking on curved roads impacts traffic stability because of geometric constraints and centrifugal forces, however, this key factor remains underexplored in existing models. To address this gap, we develop a new two-lane lattice model considering density-dependent overtaking for curved roads. The linear stability criterion of the new model is derived by stability analysis. Using nonlinear analysis, we analyze the evolution of traffic flow near critical-point, derive the mKdV equation's existence conditions and obtain the solutions of density wave. On this basis, the phase transition laws under different overtaking ratios are analyzed. Results show that at low overtaking ratios satisfying mKdV conditions, the phase diagram includes no-jam and kink-jam regions with phase transitions between them. Under these conditions, traffic congestion propagates as kink-antikink waves. However, when the overtaking ratio exceeds a specific threshold, a chaotic jam region will be added to the phase diagram. In this situation, traffic congestion evolves as kink or chaotic jams, with phase transitions shifting among free-flow, kink-antikink, and chaotic congestion phases. In addition, the research also reveals how density-dependent overtaking parameters and road curvature radius influence traffic stability and phase transitions. Finally, Numerical simulations verify the theoretical results.

Suggested Citation

  • Tian, Chuan & Kang, Yi-rong, 2025. "Density-dependent overtaking and its impact on chaotic jam and phase transitions in a two-lane lattice model on curved roads," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p3:s0960077925009245
    DOI: 10.1016/j.chaos.2025.116911
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    References listed on IDEAS

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