Dynamics of a 2D Piecewise Linear Braess Paradox Model: Effect of the Third Partition
Dynamics of a 2D Piecewise Linear Braess Paradox Model: Effect of the Third Partition
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DOI：
10.1142/s0218127415300311
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发表时间：
2015-10
期刊：
影响因子：
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通讯作者：
V. Avrutin;Christoph Dibak;A. Forno;U. Merlone
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文献类型：
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作者：
V. Avrutin;Christoph Dibak;A. Forno;U. Merlone
在这项工作中，我们研究了一个分段线性的二维不连续映射建模一个简单的网络显示Braess悖论的动力学。这个悖论代表了一个例子，在一个特定的拥挤的交通网络中增加一条新的路线，使所有的旅行者在他们的个人旅行时间方面变得更糟。在特定的情况下，其中建模的网络对应于一个二元选择的情况下，该地图被定义在两个分区和其动态已经描述。在一般情况下，对应于一个三元选择，第三分区出现导致显着更复杂的分叉结构形成的边界碰撞分叉的稳定周期与点位于所有三个分区。考虑到一个地图上的分区之一，我们提供了第一个系统的描述可能的动态这种情况下。
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.