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Abstract
We consider a general class of car-following models. Such models were studied over the last decades both on a circular and on an infinite road. Many interesting phenomena have been studied, e.g. loss of stability and stop and go waves. Whereas there is good mathematical understanding for the circular road, for the infinite road only partial results are available. In this paper we study a general approach to obtain solutions which are valid for the different settings mentioned above. The well known solutions on the circular road can be seen as a subclass of solutions, the known approaches on the infinite lane can be identified and new solutions on the infinite lane are studied. Beside the classical tools from linear analysis we will employ nonlinear bifurcation techniques. Throughout the paper as a prominent example we will use the so-called optimal velocity model proposed in Bando, et al. [1995. “Dynamical model of traffic congestion and numerical simulation.” Physical Review E 51 (2): 1035–1042].
Disclosure statement
No potential conflict of interest was reported by the author(s).