This study explores the long-standing question about the survival of noise traders in financial markets through the relatively new method of agent-based modeling. We find that, in the normal case, there are two attractors for the ratio of experts versus noise traders. Either experts disappear almost entirely from the market, or they account for a certain fraction, with noise traders still being present. In the dynamic framework, the dynamics switches between these attractors, which leads to the emergence of some typical statistical features of financial markets, such as long memory, leptokurtic returns, and bubbles and crashes. Furthermore, we achieve a general approximation of the attractors and of the switching point in between from relevant determinants.