  We formulate a model that describes the escape dynamics in a leaky chaotic
system in which the size of the leak depends on the number of the in-falling
particles. The basic motivation of this work is the astrophysical process which
describes the planetary accretion. In order to study the dynamics generally,
the standard map is investigated in two cases when the dynamics is fully
hyperbolic and in the presence of KAM islands. In addition to the numerical
calculations, an analytic solution to the temporal behavior of the model is
also derived. We show that in the early phase of the leak expansion, as long as
there are enough particles in the system, the number of survivors deviates from
the well-known exponential decay. Furthermore, the analytic solution returns
the classical result in the limiting case when the number of particles does not
affect the leak size.
