Complex Price Dynamics in a Financial Market with Imitation

In this work a simple financial model with fundamentalists and imitators is being considered. In order to describe the price dynamics of the heterogeneous stock market, a synergetic approach is used and some global bifurcations arising in the model are being studied. It is shown that the fundamental equilibrium point P* may be destabilized through a subcritical Neimark–Sacker bifurcation and that two invariant closed curves, one attracting and one repelling, appear when P* is still stable. This particular bifurcation scenario allows us to show some noticeable features of the market that emerge when the imitation effect is emphasized. Among these features are, for instance, the volatility clusters associated with the presence of multistability (i.e. coexistence of attractors) and the hysteresis phenomenon.