  We study the statistical properties of resonance widths and spacings in an
open system of interacting fermions at the transition between isolated and
overlapping resonances, where a radical change in the width distribution
occurs. Our main interest is to reveal how this transition is influenced by the
onset of chaos in the internal dynamics as the strength of random two-body
interaction between the particles increases. We have found that in the region
of overlapped resonances, the fluctuations of the widths (rather than their
mean values) are strongly affected by the onset of an internal chaos. The
results may be applied to the analysis of neutron cross sections, as well as in
the physics of mesoscopic devices with strongly interacting electrons.
