@article {ART-2015-12,
   author = {Viktor Avrutin and Christoph Dibak and Arianna Dal Forno and Ugo Merlone},
   title = {{Dynamics of a 2D Piecewise Linear Braess Paradox Model: Effect of the Third Partition}},
   journal = {International Journal of Bifurcation and Chaos},
   publisher = {World Scientific},
   volume = {25},
   number = {11},
   pages = {1530031--1530031},
   type = {Article in Journal},
   month = {October},
   year = {2015},
   doi = {10.1142/S0218127415300311},
   language = {English},
   cr-category = {G.0 Mathematics of Computing General},
   department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding},
   abstract = {In this work, we investigate the dynamics of a piecewise linear 2D
      discontinuous map modeling a simple network showing the Braess paradox. This
      paradox represents an example in which adding a new route to a specific
      congested transportation network makes all the travelers worse off in terms of
      their individual travel time. In the particular case in which the modeled
      network corresponds to a binary choice situation, the map is defined on two
      partitions and its dynamics has already been described. In the general case
      corresponding to a ternary choice, a third partition appears leading to
      significantly more complex bifurcation structures formed by border collision
      bifurcations of stable cycles with points located in all three partitions.
      Considering a map taking a constant value on one of the partitions, we provide
      a first systematic description of possible dynamics for this case.},
   url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2015-12&engl=1}
}