  We study the front propagation in Reaction-Diffusion systems whose reaction
dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We
have examined the influence of chaos and noise on the front propagation speed
and on the wandering of the front around its average position. Assuming that
the reaction term acts periodically in an impulsive way, the dynamical
evolution of the system can be written as the convolution between a spatial
propagator and a discrete-time map acting locally. This approach allows us to
perform accurate numerical analysis. They reveal that in the pulled regime the
front speed is basically determined by the shape of the map around the unstable
fixed point, while its chaotic or noisy features play a marginal role. In
contrast, in the pushed regime the presence of chaos or noise is more relevant.
In particular the front speed decreases when the degree of chaoticity is
increased, but it is not straightforward to derive a direct connection between
the chaotic properties (e.g. the Lyapunov exponent) and the behaviour of the
front. As for the fluctuations of the front position, we observe for the noisy
maps that the associated mean square displacement grows in time as $t^{1/2}$ in
the pushed case and as $t^{1/4}$ in the pulled one, in agreement with recent
findings obtained for continuous models with multiplicative noise. Moreover we
show that the same quantity saturates when a chaotic deterministic dynamics is
considered for both pushed and pulled regimes.
