Revisiting the Limit Behaviour of ``El Botellon"

Emergent phenomena occur due to the pattern of non-linear and distributed local interactions between the elements of a system over time. An example of such phenomena is the spontaneous self-organisation of drinking parties in the squares of cities in Spain, also known as El Botellon". The emergence of self-organisation was shown to depend critically on the chat-probability, i.e. the probability that a person finds someone to chat with in a square of the city. We consider a variant of El Botellon" in which this probability is instead defined based on the socialisation level. For this variant it is possible to derive the mean field limit and perform a stability analysis of the related ODE. We also provide a process algebraic model of ``El Botellon" and show that the phase plots of the ODE derived from the latter correspond very well to the mean field limit even for finite though relatively large populations.