Bifurcations and Chaos for 2D Discontinuous Dynamical Model of Financial Markets

Abstract

We develop a financial market model with interacting chartists and fundamentalists and chase sellers, the model dynamics is driven by a two-dimensional discontinuous piecewise linear map. Assume that the fixed point on the left side of border is restricted to regular saddle, we provide a more or less complete analytical treatment of the model dynamics by characterizing its possible outcomes in parameter space. The interpretation of structure for basin boundary and chaotic attractor is given by using contact bifurcation resulting from the contact between invariant set and the border. The critical value of occurring boundary crisis is given. In addition, we show that quite different scenarios can trigger real world phenomena such as bull and bear market dynamics and excess volatility.