A Bogdanov-Takens bifurcation in generic continuous second order traffic flow models

Armando Carrillo, Joaquín Delgado, Patricia Saavedra, Rosa Maria Velasco, Fernando Verduzco

Research output: Contribution to conferencePaper

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. © Springer-Verlag Berlin Heidelberg 2013.
Original languageAmerican English
Pages15-25
Number of pages11
DOIs
StatePublished - 1 Jan 2013
EventTraffic and Granular Flow 2011 -
Duration: 1 Jan 2013 → …

Conference

ConferenceTraffic and Granular Flow 2011
Period1/01/13 → …

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