Homoclinic bifurcations in heterogeneous market models

We analyze a class of models representing heterogeneous agents with adaptively rational rules. The models reduce to noninvertible maps of R2. We investigate particular kinds of homoclinic bifurcations, related to the noninvertibility of the map. A first one, which leads to a strange repellor and basins of attraction with chaotic structure, is associated with simple attractors. A second one, the homoclinic bifurcation of the saddle fixed point, also associated with the foliation of the plane, causes the sudden transition to a chaotic attractor (with self-similar structure).