Endogeneous Versus Exogeneous Shocks in Systems with Memory

Abstract

Systems with long-range persistence and memory are shown to exhibit different precursory as well as recovery patterns in response to shocks of exogeneous versus endogeneous origins. By endogeneous, we envision either fluctuations resulting from an underlying chaotic dynamics or from a stochastic forcing origin which may be external or be an effective coarse-grained description of the microscopic fluctuations. In this scenario, endogeneous shocks result from a kind of constructive interference of accumulated fluctuations whose impacts survive longer than the large shocks themselves. As a consequence, the recovery after an endogeneous shock is in general slower at early times and can be at long times either slower or faster than after an exogeneous perturbation. This offers the tantalizing possibility of distinguishing between an endogeneous versus exogeneous cause of a given shock, even when there is no ``smoking gun.'' This could help in investigating the exogeneous versus self-organized origins in problems such as the causes of major biological extinctions, of change of weather regimes and of the climate, in tracing the source of social upheaval and wars, and so on. Sornette, Malevergne and Muzy have already shown how this concept can be applied concretely to differentiate the effects on financial markets of the Sept. 11, 2001 attack or of the coup against Gorbachev on Aug., 19, 1991 (exogeneous) from financial crashes such as Oct. 1987 (endogeneous).