Chaos and bifurcation in dynamical evolution process of traffic assignment with flow “mutation”

Considering such a fact that the traffic demands freshly entering a network do not have perfect information about traffic condition and may then choose routes randomly, in this paper, we present an improved network traffic flow evolution model. The model’s properties and fixed points are investigated. Numerical results obtained from a grid network show that the system can converge to one or more fixed points without requiring of positive route flows at initial time, and can be used to approximately simulate the process of realizing user equilibrium state. It is found that oscillations and such apparently irregular behaviors as chaos occur when the model parameter representing intensity of adjusting route flow and OD demand exceeds some values. Bifurcation diagrams of some route flows and OD demands with respect to this model parameter are presented.