Abstract
The challenge to understand the dynamics of Complex Systems is attracting attention from a wide range of disciplines across the natural, biological and social sciences. Recent turmoil in the financial markets has brought this challenge into the public domain, with speculation rife as to the root cause of the observed fluctuations. At their heart, all Complex Systems share the common property of featuring many interacting objects from which the observed macroscopic dynamics emerge. Exactly how this happens cannot yet be specified in a generic way — however, an important milestone in this endeavor is to develop a quantitative understanding of any internal clustering dynamics within the population. Coalescence-fragmentation processes have been studied widely in conventional chemistry and physics — however, collective behavior in social systems is not limited by nearest-neighbor interactions, nor are the details of social coalescence or fragmentation processes necessarily the same as in physical and biological systems. Here we discuss the general phenomenon of coalescence and fragmentation problems with a focus on social systems in which a typical fragmentation process corresponds to an entire group breaking up, as opposed to the typical binary splitting studied in physical and biological systems. Having discussed situations under which power-laws for the group distribution size emerge from such internal clustering dynamics, we move on to look at the specific application to financial markets. We propose a new model for financial market dynamics based on the combination of internal clustering (i.e. herding) dynamics with human decision-making. The resulting fluctuation in price movements is closer to what is observed empirically, leading us to speculate that the combination of dynamical clustering and decision-making are key for developing quantitative models of social dynamical phenomena.
