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

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

*Autor correspondiente de este trabajo

Producción científica: Contribución a una conferenciaArtículorevisión exhaustiva

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 originalInglés
Páginas15-25
Número de páginas11
DOI
EstadoPublicada - 2013
Evento9th Conference on Traffic and Granular Flow, TGF 2011 - Moscow, Federación de Rusia
Duración: 28 sep. 20111 oct. 2011

Conferencia

Conferencia9th Conference on Traffic and Granular Flow, TGF 2011
País/TerritorioFederación de Rusia
CiudadMoscow
Período28/09/111/10/11

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