A Bogdanov–Takens Bifurcation in Generic Continuous Second Order Traffic Flow Models

Armando Carrillo (), Joaquín Delgado (), Patricia Saavedra, Rosa Maria Velasco () and Fernando Verduzco ()
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Armando Carrillo: Universidad de Sonora, Mathematics Department
Joaquín Delgado: UAM–Iztapalapa, Mathematics Department
Patricia Saavedra: UAM–Iztapalapa, Mathematics Department
Rosa Maria Velasco: UAM–Iztapalapa, Physics Department
Fernando Verduzco: Universidad de Sonora, Mathematics Department

A chapter in Traffic and Granular Flow '11, 2013, pp 15-25 from Springer

Abstract: Abstract We consider the continuous model of Kerner–Konhäuser for traffic flow given by a second order PDE for the velocity and density. Assuming conservation of cars, traveling waves solution of the PDE are reduced to a dynamical system in the plane. We describe the bifurcations set of critical points and show that there is a curve in the set of parameters consisting of Bogdanov–Takens bifurcation points. In particular there exists Hopf, homoclinic and saddle node bifurcation curves. For each Hopf point a one parameter family of limit cyles exists. Thus we prove the existence of solitons solutions in the form of one bump traveling waves.

Keywords: Traffic Flow; Travel Wave Solution; Saddle Node Bifurcation; Saddle Node; Fundamental Diagram (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-39669-4_2

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DOI: 10.1007/978-3-642-39669-4_2

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