Resumen
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.
Idioma original | Inglés |
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Páginas | 15-25 |
Número de páginas | 11 |
DOI | |
Estado | Publicada - 2013 |
Evento | 9th Conference on Traffic and Granular Flow, TGF 2011 - Moscow, Federación de Rusia Duración: 28 sep. 2011 → 1 oct. 2011 |
Conferencia
Conferencia | 9th Conference on Traffic and Granular Flow, TGF 2011 |
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País/Territorio | Federación de Rusia |
Ciudad | Moscow |
Período | 28/09/11 → 1/10/11 |