A discrete time car following model and the bi-parameter logistic map

A discrete time model for car following behaviour is investigated. It is found that the model can be expressed in the form of a logistic map with multiple control parameter values. The case where the logistic map has a bi-value control parameter is investigated and relevant Feigenbaum diagrams are presented and the behaviour of the Lyapunov exponent is investigated. Divergent behaviour in the chain of vehicles is also considered.