Generalized Communicating P Systems Working in Fair Sequential Model

TL;DR

This paper introduces a new sequential and fair derivation mode for generalized communicating P systems, linking them to population protocols and stochastic models, and describing their dynamics via ODEs in large populations.

Contribution

It presents a novel derivation mode for GCPS aligned with population protocols and connects stochastic evolution to Gillespie's SSA, enabling ODE-based analysis.

Findings

PP can be modeled as a specific GCPS variant

Stochastic evolution corresponds to Gillespie's SSA

GCPS dynamics can be described by ODEs for large populations

Abstract

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. We show that PP can be seen as a particular variant of GCPS. We also consider a particular stochastic evolution satisfying the fairness condition and obtain that it corresponds 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.