This paper examines the emergence of complex volatility in dynamic asset ma
rkets when there are heterogeneous agents. A discrete formulation is studie
d with two categories of market participants, fundamentalist traders who bu
y when the asset price is below the fundamental value and sell when it is a
bove and noise traders who use moving average technical trading rules that
can lead them to chase trends. Agents switch from one type of strategy to t
he other according to relative returns. A variety of outcomes are studied u
sing numerical simulation, including variation of market price responsivene
ss to changes in excess demand, in switching behavior, and the introduction
of noise. Bifurcation analysis of certain parameters is presented.