  We consider heteroclinic attractor networks motivated by models of
competition between neural populations during binocular rivalry. We show that
Gamma distributions of dominance times observed experimentally in binocular
rivalry and other forms of bistable perception, commonly explained by means of
noise in the models, can be achieved with quasi-periodic perturbations. For
this purpose, we present a methodology based on the separatrix map to model the
dynamics close to heteroclinic networks with quasi-periodic perturbations. Our
methodology unifies two different approaches, one based on Melnikov integrals
and another one based on variational equations. We apply it to two models:
first, to the Duffing equation, which comes from the perturbation of a
Hamiltonian system and, second, to a heteroclinic attractor network for
binocular rivalry, for which we develop a suitable method based on Melnikov
integrals for non-Hamiltonian systems. In both models, the perturbed system
shows chaotic behavior while dominance times achieve good agreement with Gamma
distributions. Moreover, the separatrix map provides a new (discrete) model for
bistable perception which, in addition, replaces the numerical integration of
time-continuous models and, consequently, reduces the computational cost and
avoids numerical instabilities.
