  Based on the classical traffic model by Greenberg, a linear differential
equation, we analyze it by means of varying the critical velocity $v_o$ that
appears in it as a parameter. In order to make such analysis we have obtained a
solution for such a model and discretized it, obtaining related expressions for
density $k$, flow $q$ and velocity $v$ to be treated as paired functions to
obtained maps in phase-planes in which it is possible to observe distinct
behaviors which span from monotonic and oscillatory stable trajectories, limit
cycles of distinct periodicity, and chaotic ones. These behaviors are analyzed
from a dynamical approach and then ilustrated with simulations performed in
each case. As it is shown in this paper, these analyses are similar to those
carried out in similar though simpler expressions (i.e. logistic-type
functions), but taking in this case a new and direct approach through a
nonlinear expression not used before to perform studies like these presented in
this document, with a deep detail in the manner in which traffic variables are
involved qualitatively and quantitatively.
