A traffic flow model with overtaking as a Filippov system

• Autores: Lubor Buric, Vladimír Janovský
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 254, Nº 1, 2013 (Ejemplar dedicado a: Nonlinear Elliptic Differential Equations, Bifurcation, Local Dynamics of Parabolic Systems and Numerical Methods), págs. 55-64
• Idioma: inglés
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• Resumen

  • Weinvestigate microscopic models of road traffic. In particular,weconsider a car-following model for a single-line traffic flow of N identical cars on a circular road. The classical differentiable model breaks down at the time instant when two cars collide. However, the natural action of a driver would be to overtake a slower car. In our previous work, we proposed a model which simulates the overtaking.Weobserved a large variety of oscillatory solutions (oscillatory patterns) of the model. In the present contribution, we formulate our model as a particular Filippov system, i.e., ODEs with discontinuous right hand sides.

    Hence, we can identify our problem with a well defined solution class.Wedefine oscillatory patterns as invariant objects of this Filippov system.