  A symmetrical cubic discrete coupled logistic equation is proposed to model
the symbiotic interaction of two isolated species. The coupling depends on the
population size of both species and on a positive constant $\lambda$, named the
mutual benefit. Different dynamical regimes are obtained when the mutual
benefit is modified. For small $\lambda$, the species become extinct. For
increasing $\lambda$, the system stabilizes in a synchronized state or
oscillates in a 2 periodic orbit. For the greatest permitted values of
$\lambda$, the dynamics evolves into a quasiperiodic, into a chaotic scenario
or into extinction. The basins for these regimes are visualized as coloured
figures on the plane. These patterns suffer different change as consequence of
basins' bifurcations. The use of the critical curves let us to determine the
influence of the zones with different number of first rank preimages in those
bifurcation mechanisms.
