Memory Oscillator for Modeling Socio-economic Oscillatory Responses to Extreme Events

The reaction of markets and people to extreme events is studied with respect to their. oscillations following the occurring after a severe perturbation. The phenomenon is modeled with a pseudo memory-damped accelerator. It is the case of the people, mostly peasants, returning to their homes after leaving them as a consequence of the 1951 Po River flood in Polesine (Italy), of the variation of the number of Revenue Passenger Miles (RPM) in the US after the 2001 September 11(th) terrorist attack in New York, of the number of abortions in Italy following the 1978 law which legalized the abortions and of the embezzlement crimes in Italy during the clean hands period at the end of the last century. We verified that in the four cases the return to normality had similar features: the number of individuals affected by the extreme event had a step-like variation followed by oscillation with decreasing amplitude. The assumption is that the evolution of a market or population may be governed by an equation similar to that of an oscillator including a memory formalism, and that the extreme event is the delta function which generates the Green function. We also show how the memory may stabilize the market or the population, when the perturbation is constant while an increasing perturbation may lead to a crisis. We estimate the parameters characterizing the effects of the extreme event of the 2001 September 11(th) terrorist attack and of the 1978 abortion law in Italy.