In this paper we study some global bifurcations arising in a heterogeneous financial model with fundamentalists and imitators. Such bifurcations which cause the appearance and disappearance of closed invariant curves (attracting or repelling) involve the stable and unstable sets of a saddle cycle with consequent changes in their dynamic behavior. Numerical investigations show that the transition between two qualitatively different regimes are characterized by the occurrence of homoclinic tangles with chaotic dynamics.
Foroni, I., Agliari, A. (2011). Complex dynamics associated with the appearance/disappearance of invariant closed curves. MATHEMATICS AND COMPUTERS IN SIMULATION, 81(8), 1640-1655 [10.1016/j.matcom.2010.12.008].
Complex dynamics associated with the appearance/disappearance of invariant closed curves
FORONI, ILARIA;
2011
Abstract
In this paper we study some global bifurcations arising in a heterogeneous financial model with fundamentalists and imitators. Such bifurcations which cause the appearance and disappearance of closed invariant curves (attracting or repelling) involve the stable and unstable sets of a saddle cycle with consequent changes in their dynamic behavior. Numerical investigations show that the transition between two qualitatively different regimes are characterized by the occurrence of homoclinic tangles with chaotic dynamics.
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