On the Appearance and Bifurcations of Weird Quasiperiodic Attractors in a Financial Market Model

We consider a financial market model in which the market maker sets prices based on orders placed by chartists and fundamentalists. To sustain profitability, the market maker adjusts prices more strongly when price fluctuations become too calm. The dynamics of this model is described by a two-dimensional discontinuous piecewise-linear map that generates endogenous oscillations. Interestingly, this dynamics appears chaotic but is in fact quasiperiodic, corresponding to a recently discovered new kind of attractor, which we call a Weird Quasiperiodic Attractor (WQA). The bifurcation mechanisms leading to these attractors are not yet fully understood. Here, we describe some mechanisms underlying the appearance and disappearance of WQAs, related to eigenvectors of a particular composite map, as well as contact bifurcations leading to changes in the structure of WQAs.