Abstract
A theoretical framework is laid out, where a Stock Exchange is represented as a process under decentralized control. Attention is devoted to a specific case, in which the trading activity is described by a second order dynamical system. Three economically significant modes of behavior are identified. The stock market can (1) adjust to a stable equilibrium, (2) approach a stable limit cycle, (3) diverge to infinity. The transition from mode (1) to mode (2) is a supercritical Hopf bifurcation, whereas the transition from mode (2) to mode (3) is a homoclinic bifurcation.