Dynamics of bimodality in vehicular traffic flows

TL;DR

This paper introduces a mathematical model capturing bimodal traffic flow patterns, analyzing the conditions for symmetry breaking and transitions to unimodal distributions, revealing complex dynamical behaviors.

Contribution

It presents a novel model equation for bimodal traffic flows and analyzes the bifurcation conditions leading to symmetry breaking and unimodal transitions.

Findings

Identification of a fixed point linked by a homoclinic trajectory

Mathematical conditions for bimodality established

Analysis of bifurcation leading to unimodal behavior

Abstract

A model equation has been proposed to describe bimodal features in vehicular traffic flows. The dynamics of the bimodal distribution reveals the existence of a fixed point that is connected to itself by a homoclinic trajectory. The mathematical conditions associated with bimodality have been established. The critical factors necessary for both a breaking of symmetry and a transition from bimodal to unimodal behaviour, in the manner of a bifurcation, have been analysed.