Dynamic response and transfer function of social systems: A neuro-inspired model of collective human activity patterns

Abstract

The interaction of social networks with the external environment gives rise to non-stationary activity patterns reflecting the temporal structure and strength of exogenous influences that drive social dynamical processes far from an equilibrium state. Following a neuro-inspired approach, based on the dynamics of a passive neuronal membrane, and the firing rate dynamics of single neurons and neuronal populations, we build a state-of-the-art model of the collective social response to exogenous interventions. In this regard, we analyze online activity patterns with a view to determining the transfer function of social systems, that is, the dynamic relationship between external influences and the resulting activity. To this end, first we estimate the impulse response (Green’s function) of collective activity, and then we show that the convolution of the impulse response with a time-varying external influence field accurately reproduces empirical activity patterns. To capture the dynamics of collective activity when the generating process is in a state of statistical equilibrium, we incorporate into the model a noisy input convolved with the impulse response function, thus precisely reproducing the fluctuations of stationary collective activity around a resting value. The outstanding goodness-of-fit of the model results to empirical observations, indicates that the model explains human activity patterns generated by time-dependent external influences in various socio-economic contexts. The proposed model can be used for inferring the temporal structure and strength of external influences, as well as the inertia of collective social activity. Furthermore, it can potentially predict social activity patterns.