This paper proposes a coupled map car-following traffic model, which describes a dynamical behavior of a group of road vehicles running in a single lane without overtaking. This model consists of a lead vehicle and following vehicles, which have a piecewise linear optimal velocity function. When the lead-vehicle speed is varied, we can observe a traffic jam in the group of the vehicles. We derive a condition under which the traffic jam never occurs in our model. Furthermore, in order to suppress the traffic jam, for each vehicle we use a dynamic version of decentralized delayed-feedback control proposed in [Konishi, Hirai, and Kokame, Phys. Rev. E 58, 3055 (1998)], and provide a systematic procedure for designing the controller.
The present paper shows that dynamic coupling induces amplitude death in coupled identical oscillators. For a simple limit-cycle oscillator, our theoretical analysis provides the necessary and sufficient condition for amplitude death. Furthermore, we guarantee that amplitude death never occurs, if each oscillator satisfies the odd number property that is known in the field of delayed-feedback control of chaos.
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