Controlling Chaos Through Local Knowledge

Despite canonical behavioural financial market models [Day R, Huang W. Bulls, bears and market sheep. J Econ Behav Org 1990;14:299–329], that use different types of agents (i.e., fundamentalist vs. chartists), we develop a model in which the source of instability is the interaction of groups that are homogeneous in the strategy they use, but have heterogeneous beliefs about the fundamental value of the asset. Specifically, heterogeneity arises among two groups of fundamentalists that follow gurus. We show that an increasing distance between beliefs (the degree of heterogeneity), leads first (i) to a pitchfork bifurcation to arise secondly (ii) it generates, together with a larger reaction to misalignment of both market maker and agents, the appearance of a periodic, or even, chaotic, price fluctuation; (iii) finally a homoclinic bifurcation [Dieci R, Bischi GI, Gardini L. From bi-stability to chaotic oscillations in a macroeconomic model. Chaos, Solitons & Fractals 2001;12:805–22] transforms a two piece chaotic set into a one piece chaotic set that generates bull and bear markets