In order to describe the dynamics of a group of road vehicles travelli
ng in a single lane, car-following models attempt to mimic the interac
tions between individual vehicles where the behaviour of each vehicle
is dependent upon the motion of the vehicle immediately ahead. In this
paper we investigate a modified car-following model which features a
new nonlinear term which attempts to adjust the inter-vehicle spacing
to a certain desired value. In contrast to our earlier work, a desired
time separation between vehicles is used rather than simply being a c
onstant desired distance. Zn addition, we extend our previous work to
include a non-zero driver vehicle reaction time, thus producing a more
realistic mathematical model of congested road traffic. Numerical sol
ution of the resulting coupled system of nonlinear delay differential
equations is used to analyse the stability of the equilibrium solution
to a periodic perturbation. For certain parameter values the post-tra
nsient response is a chaotic (nonperiodic) oscillations consisting of
a broad spectrum of frequency components. Such chaotic motion leads to
highly complex dynamical behaviour which is inherently unpredictable.
The model is analysed over a range of parameter values and, in each c
ase, the nature of the response is indicated. In the case of a chaotic
solution, the degree of chaos is estimated.