  Context: The brightness of FUors increases by several magnitudes within one
to several years. The currently favoured explanation for this brightness boost
is that of dramatically rising accretion from the disc material around a young
star. The mechanism leading to this accretion increase is a point of debate.
Aims: Choosing the Orion Nebula Cluster as representative we simulate accretion
bursts driven by encounters in dense stellar environments. We investigate
whether properties like rise and decay times, event frequency etc. speak for
encounters as a possible cause for FUor phenomena. Method: We combine cluster
simulations performed with the Nbody6++ code with particle simulations that
describe the effect of a fly-by on the disc around a young star to determine
the induced mass accretion. Results: The induced accretion rates, the overall
temporal accretion profile, decay time and possibly the binarity rate we obtain
for encounter-induced accretion agree very well with observations of FUors.
However, the rise-time of one year observed in some FUors is difficult to
achieve in our simulations unless the matter is stored somewhere close to the
star and then released after a certain mass limit is transgressed. The severest
argument against the FUors phenomenon being caused by encounters is that most
FUors are found in environments of low stellar density. We extend the
discussion to eccentric binaries and gravitationally unstable discs and find
that both models have similar problems in achieving the necessary rise-times.
Conclusions: We predict that in dense young clusters these outbursts should
predominantly happen close to the cluster center and with large mass ratios
between the involved stars.(abridged)

Astrophysics