A note on biased fundamentalists

In this note, we report a result not recognized in the model analyzed in Naimzada and Ricchiuti (2009) [1]: heterogeneity may have an ambiguous role in the complex dynamics. Indeed, given high reactivity of either market maker or agents, an increasing heterogeneity initially stabilizes the price (through a subcritical period two cycle) and then it destabilizes the price (initially through a pitchfork bifurcation). Moreover, we define better the structure of beliefs, highlighting their position in comparison with a unique (not observed) fundamental value and assuming that agents are pure biased traders.

► Heterogeneity may play an ambiguous role in complex dynamics.
► An increasing heterogeneity initially stabilizes and then destabilizes the price.
► Higher heterogeneity generates the occurrence of a chaotic price fluctuation.
► Through an homoclinic bifurcation, bull and bear markets can be generated.