Generalized Communicating P Systems Working in Fair Sequential Mode

In this article we consider a new derivation mode for generalized communicating P systems (GCPS) corresponding to the functioning of population protocols (PP) and based on the sequential derivation mode and a fairness condition that permits to ensure a particular sequence of configurations. We show that PP can be seen as a particular variant of GCPS.We also consider several stochastic evolutions satisfying different fairness conditions and particularly focus on those corresponding to the run of a Gillespie's SSA. This permits to further describe the dynamics of GCPS by a system of ODEs when the population size goes to the infinity.