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.
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1142/S0218127415300311|
|Codice identificativo ISI:||WOS:000363733700003|
|Codice identificativo Scopus:||2-s2.0-84945952893|
|Titolo:||Dynamics of a 2D Piecewise Linear Braess Paradox Model: Effect of the Third Partition|
|Appare nelle tipologie:||1.1 Articolo in rivista|