On delay-induced oscillations in a coupled traffic-behavior evolutionary dynamics system

Abstract

This letter develops a coupled traffic-behavior model to study the interaction between driver strategy evolution and urban road congestion. Drivers choose cooperative or selfish strategies, while traffic conditions are represented by a normalized congestion density. A behavioral response delay τ is introduced to capture delayed adaptation to past congestion information. The equilibria and their local stability are analyzed, and the Hopf bifurcation condition of the mixed equilibrium is derived. Numerical results show that a small delay leads to convergence to the mixed equilibrium, whereas a sufficiently large delay causes persistent oscillations in congestion and cooperation. The delayed feedback strength and behavioral parameters also affect the oscillation amplitude, equilibrium cooperation level, and critical delay. These findings show that delayed behavioral responses can generate collective oscillations in coupled traffic systems.