Speculative behavior and chaotic asset price dynamics: On the emergence of a bandcount accretion bifurcation structure

Abstract

We study a simple financial market model with interacting chartists and fundamentalists that may give rise to multiband chaotic attractors. In particular, asset prices fluctuate erratically around their fundamental values, displaying a significant bull and bear market behavior. An in-depth analytical and numerical study of our model furthermore reveals the emergence of a new bifurcation structure, a phenomenon that we call a bandcount accretion bifurcation structure. The latter consists of regions associated with chaotic dynamics only, the boundaries of which are not defined by homoclinic bifurcations, but mainly by contact bifurcations of particular type where two distinct critical points of certain ranks coincide.

Border collision bifurcations of chaotic attractors in one-dimensional maps with multiple discontinuities

“…A few further substructures can also be recognized, as for example the small trapezoidal-shaped regions in figure 2a situated around μ L = 3. Similar structures have been reported in [41]. It is also clearly visible in figure 2b that Regions corresponding to multi-band chaotic attractors with one, two, .…”

“…The goal of the present work is more modest, namely, to describe two novel bifurcation mechanisms occurring to chaotic attractors in one-dimensional maps with multiple discontinuities. Note that some of these mechanisms have been reported for the first time in [41], within the context of an applied model from the field of economics.…”