A Hybrid Automata model of social networking addiction

At the neurological level, the Dopamine System plays a key role in addiction processes. Mathematical models of the Dopamine System have been proposed to study addiction to nicotine, drugs and gambling. In this paper, we propose a Hybrid Automata model of the Dopamine System, based on the mathematical model proposed by Gutkin et al. Our model allows different kinds of addiction causes to be described. In particular, we consider the problem of Internet addiction and its spread through interaction on social networks. This study is undertaken by performing simulations of virtual social networks by varying the network topology and the interaction propensity of users. We show that scale-free networks favour the emergence of addiction phenomena, in particular when users having a high propensity to interaction are present. We propose also variants of our model in which the propensity of a user to interact in a social network may vary over time, either caused by social imitation or by "social sitting".