Chaos and dynamical transition of a single vehicle induced by traffic light and speedup

We study the dynamical behavior of a single vehicle moving through a sequence of traffic lights, where the vehicle speeds up to retrieve the delay induced by traffic lights and the traffic lights turn on and off periodically on a single-lane highway. The dynamical model of the vehicle controlled by both speedup and traffic light is expressed in terms of the nonlinear map. The motion of vehicle is controlled by two parameters: cycle time and speedup rate. When the speedup rate is higher than the critical value, the vehicle exhibits chaotic motion. The vehicle moves chaotically even if the model is deterministic. By varying both parameters, the complex dynamical transitions among the regular, periodic, and chaotic motions of the vehicle occur. The dynamical transitions between the complex motions are clarified.