Homoclinic bifurcations in heterogeneous market models |
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| Affiliation: | 1. University of Kansas, Lawrence, and Center for Financial Stability, New York City, USA;2. University of Cagliari, Italy;3. Indira Gandhi Institute of Development Research, Mumbai, India;4. University of Cagliari, Italy;5. University of Cagliari, Italy;1. Department of Economics and Social Science, Catholic University, Via Emilia Parmense 84, 29100 Piacenza, Italy;2. Department of Economics and Finance, Catholic University, Largo Gemelli 1, 20100, Milano, Italy |
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| Abstract: | 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). |
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