ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Dynamics of Bimodality in Vehicular Traffic Flows

Journal of Applied Nonlinear Dynamics 3(1) (2014) 17--26 | DOI:10.5890/JAND.2014.03.002

Arjun Mullick$^{1}$; Arnab K. Ray$^{2}$

$^{1}$ Department of Computer Science and Engineering, Jaypee University of Engineering and Technology, Raghogarh, Guna 473226, Madhya Pradesh, India

$^{2}$ Department of Physics, Jaypee University of Engineering and Technology, Raghogarh, Guna 473226, Madhya Pradesh, India

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 uni-modal behaviour, in the manner of a bifurcation, have been analysed.

Acknowledgments

The authors thank R. Atre, A. Basu, J. K. Bhattacharjee and T. Naskar for some useful discussions.

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