Journal of Applied Nonlinear Dynamics
Dynamics of Bimodality in Vehicular Traffic Flows
Journal of Applied Nonlinear Dynamics 3(1) (2014) 1726  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 unimodal 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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