Chaotic and periodic motions of two competing vehicles controlled by traffic lights

We study the dynamical behavior of two vehicles moving through a sequence of traffic lights, where the traffic lights turn on and off periodically on a highway. Each vehicle speeds up or down if it is overtaken by the other vehicle or it passes over the other. The dynamical model of two vehicles controlled by both speed and traffic light is expressed in terms of the nonlinear maps. The motion of vehicles is determined by two parameters: speed's variation rate and cycle time of traffic lights. When the speed's variation rate is higher than the critical value, the vehicles exhibit the chaotic motion. The vehicles move chaotically even if the model is deterministic. By varying both parameters, the complex dynamical transitions occur among the regular, periodic, and chaotic motions. The dynamical transitions between the complex motions are clarified.