Membrane Computing as a Modeling Tool for Discrete Systems

Abstract

Problem statement: Discrete systems have been modeled by using Ordinary Differential Equation (ODE) in which the variation of concentration of an object was modeled as continuous and deterministic manner, contrary to the real behaviors of such systems. Although, this approaches able to generate the general behavior of the system, the specific discrete processes and stochastic behaviors in the system have not been addressed. Membrane computing has been an unconventional computational approach that provides a platform for modeling discrete systems. It deals with parallel, distributed and non-deterministic computing models. Approach: This study was carried to compare the ODE with membrane computing approach in modeling a discrete system by taking Prey-Predator population as the case study. Membrane computing simulator based on Gillespie Algorithm and Probabilistic and Symbolic Model Checker (PRISM) were used to verify and validate the model. Results: Membrane computing able to not only maintain the dynamics and equilibrium of Prey-Predator population but also preserve the discrete and stochastic evolvement of the prey and predator in the population by sustaining the properties of the system. Conclusion: Membrane computing modeling approach preserved the characteristics of discrete systems that absent in the ODE approach.