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 R-2. 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). (C) 2002 Elsevier Science Ltd. All rights reserved.