Log-Periodic Power Law as a Predictor of Catastrophic Events: A New Mathematical Justification

To decrease the damage caused by meteorological disasters, it is important to be able to predict these disasters as accurately as possible. One of the most promising ways of achieving such a prediction comes from the observation that in the vicinity of a catastrophic event, many parameters exhibit log-periodic power behavior, with oscillations of increasing frequency. By fitting the corresponding formula to the observations, it is often possible to predict the catastrophic event. Such successful predictions were made in many application areas ranging from ruptures of fuel tanks to earthquakes to stock market disruptions. The fact that similar formulas can be applied to vastly different systems seems to indicate that the log-periodic power behavior is not related to a specific nature of the system, it is caused by general properties of system. In this paper, we indeed provide a general system-based explanation of this law. The general character of this explanation makes us confident that this law can be also used to predict meteorological disasters. 1 Formulation of the Problem Need to predict meteorological disasters. To decrease the damage caused by meteorological disasters, it is important to be able to predict these disasters as accurately as possible.