Non-smooth transitions in a simple city traffic model analyzed through supertracks

We explore the nontrivial behavior of a particular city traffic model due to its minimalistic representation of basic city traffic dynamics. The chaotic behavior is studied through the supertrack functions, an approach that in some cases exposes more information than usual methods. In particular, we explore a parameter region that may be related to the high sensitivity of traffic flow and eventually could lead to traffic jams. First, we describe analytically a period adding region, that has a universal critical exponent of α = 1. Second, we analyze a chaotic crisis giving rise to an inverse supertrack cascade with a period scaling of α≈0.49α≈0.49. This cascade seems to be universal when approaching to the chaotic behavior, but in general it depends on the braking and accelerating capabilities of the vehicles.

► We analyzed a simple city traffic model through supertrack functions. ► We derived an analytical description of a period adding bifurcation in our model. ► We found what seems to be a new kind of crisis, which we called threshold crisis.