We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. [1] , in the case of very large populations. For the general model we give a sufficient condition for stability that can be checked in polynomial time. We also study two interesting subcases: (a) protocols whose specifications (in our terms) are configuration independent. We show that they are always stable and that their eventual subpopulation percentages are actually a Markov Chain stationary distribution. (b) protocols that have dynamics resembling virus spread. We show that their dynamics are actually similar to the well-known Replicator Dynamics of Evolutionary Games. We also provide a sufficient condition for stability in this case.
In REF , the authors study the dynamics and the stability of (probabilistic) population protocols via ordinary differential equations.
The Dynamics of Probabilistic Population Protocols
ArXiv
ArXiv
Computer Science