  In this paper, we are concerned with the permanence of a Lotka-Volterra model
of three competing species with seasonal succession. Based on the existence of
a carrying simplex, that is a globally attracting hypersurface of codimension
one, we provide a complete classification of the permanence and impermanence in
terms of inequalities on the parameters of this model. Moreover, we numerically
show that invariant closed curves can occur in the permanent classes, which
means that the positive fixed point of the associated Poincare map in the
permanent classes is not always globally asymptotically stable.
