The Memory Response of Populations and Markets to Extreme Events

This study aims to discuss and quantify the reaction of a market or a population to perturbations assuming that their behaviour is governed by a differential equation containing a memory formalism modelling their evolution. A perturbation acts on a market, as well as on a population, as the delta function to generate the Green function. In both cases the memory has a stabilising effect. In the case of markets it is seen how the memory formalisms will definitely stabilise the market when the intensity of the perturbation is small relative to the effect of the memory; when the intensity of the perturbation is larger the market may lead to an extreme event. The same would be true also for populations. As practical cases we consider the people of Polesine (Italy) returning to their homes after leaving as a consequence of the 1951 Po River flood, then we consider the variation of the number of Revenue Passenger Miles (RPM) in the US after the 2001 September 11th terrorist attack in New York and finally the number of abortions in Italy following the 1978 law legalising the abortions. It is seen that in the three cases, in spite of the differences, the return to normality had similar features: the number of individuals affected by the extreme event had an initial sudden variation followed by oscillations of decreasing amplitude. A table with the values of the parameters tentatively obtained from the population data is finally presented.