The Dynamics of Adaptive Networked Societies of Tiny Artefacts

In the near future, it is reasonable to expect that new types of systems will appear, of massive scale that will operating in a constantly changing networked environment. We expect that most such systems will have the form of a large society of tiny networked artefacts. Angluin et al. introduced the notion of "probabilistic population protocols" (PPP) in order to model the behavior of such systems where extremely limited agents are represented as finite state machines that interact in pairs under the control of an adversary scheduler. We propose to study the dynamics of probabilistic population protocols, via the differential equations approach. We provide a very general model that allows to examine the continuous dynamics of population protocols and we show that it includes the model of Angluin et al., under certain conditions, with respect to the continuous dynamics of the two models. Our main proposal here is to exploit the powerful tools of continuous nonlinear dynamics in order to examine the behavior of such systems. We also provide a sufficient condition for stability.