  In the framework of the generalized Lotka Volterra model, solutions
representing multispecies sequencial competition can be predictable with high
probability. In this paper, we show that it occurs because the corresponding
"heteroclinic channel" forms part of an attractor. We prove that, generically,
in an attracting heteroclinic network involving a finite number of hyperbolic
and non-resonant saddle-equilibria whose linearization has only real
eigenvalues, the connections corresponding to the most positive expanding
eigenvalues form a part of an attractor (observable in numerical simulations).
