  In this paper, we study in detail the structure of the global attractor for
the Lotka--Volterra system with a Volterra--Lyapunov stable structural matrix.
We consider the invasion graph as recently introduced in [19] and prove that
its edges represent all the heteroclinic connections between the equilibria of
the system. We also study the stability of this structure with respect to the
perturbation of the problem parameters. This allows us to introduce a
definition of structural stability in ecology in coherence with the classical
mathematical concept where there exists a detailed geometrical structure,
robust under perturbation, that governs the transient and asymptotic dynamics.
