Bifurcation analysis and control of the full velocity difference model with delayed velocity difference

Area of Science:

• Traffic Engineering
• Nonlinear Dynamics
• Complex Systems Analysis

Background:

• Urbanization and increased vehicle numbers lead to significant traffic congestion.
• Understanding traffic flow dynamics is crucial for developing effective mitigation strategies.
• Existing models may not fully capture the complex, nonlinear behaviors of traffic systems.

Purpose of the Study:

• To propose a macroscopic traffic flow model incorporating delayed speed differences.
• To analyze nonlinear traffic phenomena using nonlinear bifurcation theory.
• To investigate methods for controlling traffic instabilities and improving flow.

Main Methods:

• Development of a macroscopic traffic flow model based on a delayed speed difference car-following model.
• Application of traveling wave transformation to convert the car-following model to a macroscopic model.
• Utilizing linear stability analysis to identify bifurcation points and analyze traffic system stability.
• Employing density-time and phase plane diagrams for visual representation of traffic dynamics.
• Designing a feedback controller to regulate Hopf bifurcations.

Main Results:

• The proposed model theoretically demonstrates the existence of bifurcation points in traffic flow.
• Visualizations confirm sudden changes in traffic flow as parameters cross bifurcation points.
• Identification of critical points where traffic system stability transitions occur.
• The study successfully explores qualitative characteristics of inhomogeneous continuous traffic flow.

Conclusions:

• The developed macroscopic traffic flow model effectively captures nonlinear traffic phenomena.
• Nonlinear bifurcation analysis provides valuable insights into traffic system stability and instability.
• The proposed feedback controller shows potential for delaying or eliminating undesirable Hopf bifurcations.
• This research contributes to a better understanding and management of urban traffic congestion.