. . "NL - Nizozemsko" . . "2"^^ . "2014" . "1"^^ . . "RIV/00216208:11320/13:10189370" . "A traffic flow model with overtaking as a Filippov system"@en . "0377-0427" . . . "59163" . "000320894600006" . "Janovsk\u00FD, Vladim\u00EDr" . "A traffic flow model with overtaking as a Filippov system" . "We investigate microscopic models of the road traffic. In particular, we consider the 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. Nevertheless, the natural action of a driver would be to overtake the slower car. In our previous work, we proposed the model which simulates the overtaking. We observed 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 righthand sides. Hence, we can identify our problem with a well defined solution class. We define oscillatory patterns as invariant objects of this Filippov system."@en . "11320" . . . . . . . "Journal of Computational and Applied Mathematics" . "I, Z(MSM0021620839)" . "A traffic flow model with overtaking as a Filippov system"@en . . "We investigate microscopic models of the road traffic. In particular, we consider the 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. Nevertheless, the natural action of a driver would be to overtake the slower car. In our previous work, we proposed the model which simulates the overtaking. We observed 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 righthand sides. Hence, we can identify our problem with a well defined solution class. We define oscillatory patterns as invariant objects of this Filippov system." . . "piecewise smooth dynamics; Filippov system; overtaking; microscopic models; road traffic"@en . "[A2DD65DC5086]" . "Buric, Lubor" . . "2014//254" . . "A traffic flow model with overtaking as a Filippov system" . "RIV/00216208:11320/13:10189370!RIV14-MSM-11320___" . "http://10.1016/j.cam.2013.03.033" . "10"^^ . . . "10.1016/j.cam.2013.03.033" . .