A phase plane analysis method for complex nonlinear phenomena of macroscopic traffic flow

In order to analysis the complex nonlinear traffic phenomena, a new phase plane analysis method is presented in this paper by transforming the traffic flow problem into system stability problem. Variable substitution is introduced into this paper as the key method which matches traffic congestion with the unstable system. The new proposed method is used to describe various nonlinear phenomena due to different input and output conditions on ramps through an existing continuum model. The results show that the new phase plane analysis method can describe the traffic phenomena as well as the traditional methods. Moreover, the variation of density or velocity with time or sections can be described more clearly by the new method.