The scientific study of complex systems has transformed a wide range of disciplines in recent years, enabling researchers in both the natural and social sciences to model and predict phenomena as diverse as earthquakes, global warming, demographic patterns, financial crises, and the failure of...

We argue that the word ``critical'' in the title is not purely literary. Based on our and other previous work on nonlinear complex dynamical systems, we summarize present evidence, on the Oct. 1929, Oct. 1987, Oct. 1987 Hong-Kong, Aug. 1998 global market events and on the 1985 Forex event, for...

The Nasdaq Composite fell another $\approx 10 %$ on Friday the 14'th of April 2000 signaling the end of a remarkable speculative high-tech bubble starting in spring 1997. The closing of the Nasdaq Composite at 3321 corresponds to a total loss of over 35% since its all-time high of 5133 on the...

In a series of papers based on analogies with statistical physics models, we have proposed that most financial crashes are the climax of so-called log-periodic power law signatures (LPPS) associated with speculative bubbles. In addition, a large body of empirical evidence supporting this...

We develop the concept of “dragon-kings” corresponding to meaningful outliers, which are found to coexist with power laws in the distributions of event sizes under a broad range of conditions in a large variety of systems. These dragon-kings reveal the existence of mechanisms of...