  In this paper we present a continuous time dynamical model of heterogeneous
agents interacting in a financial market where transactions are cleared by a
market maker. The market is composed of fundamentalist, trend following and
contrarian agents who process information from the market with different time
delays. Each class of investor is characterized by path dependent risk
aversion. We also allow for the possibility of evolutionary switching between
trend following and contrarian strategies. We find that the system shows
periodic, quasi-periodic and chaotic dynamics as well as synchronization
between technical traders. Furthermore, the model is able to generate time
series of returns that exhibit statistical properties similar to those of the
S&P500 index, which is characterized by excess kurtosis, volatility clustering
and long memory
