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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)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

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

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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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