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 language | American English |
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Pages | 15-25 |
Number of pages | 11 |
DOIs | |
State | Published - 1 Jan 2013 |
Event | Traffic and Granular Flow 2011 - Duration: 1 Jan 2013 → … |
Conference
Conference | Traffic and Granular Flow 2011 |
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Period | 1/01/13 → … |