Heterogeneous fundamentalists and imitative processes

• Published in: Applied mathematics and computation 2008-05, Vol.199 (1), p.171-180
• Main Authors: Naimzada, Ahmad K., Ricchiuti, Giorgio
• Format: Article
• Language: English
• Subjects: Chaos; Exact sciences and technology; Financial markets; Global analysis, analysis on manifolds; Heterogeneous interacting agents; Mathematical analysis; Mathematical economics; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Partial differential equations; Sciences and techniques of general use; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2007.09.061

Developing a model with a switching mechanism, we show how complex dynamics can be generated even though heterogeneity arises among agents with the same trading rules (fundamentalists). We assume that there are two experts which are imitated by other operators. We show that (i) market instability and periodic, or even, chaotic price fluctuations can be generated; (ii) conditions exist under which an expert can drive another expert out of the market; (iii) two experts can survive when the dynamic system either generates a period doubling bifurcation around an attractor or when an homoclinic bifurcation leads to the merging of the two attractors [R. Dieci, G.I. Bischi, L. Gardini, From bi-stability to chaotic oscillations in a macroeconomic model, Chaos, Solitons and Fractals 12 (2001) 805–822]; (iv) a central role is played by the reaction to misalignment of both market maker and agents.