Investigating local evolutions in dynamical probabilistic P systems

We present a simulation tool to predict the behavior of single regions in dynamical probabilistic P systems with reduced size, that is, membrane systems with probability values associated to rules that dynamically change during the evolution, where the number of objects whose evolution is analyzed is not greater than 2. The tool is based on the construction of a grid over the phase space of a region, which is then used to evaluate the mean displacement of each multiset in the grid and to build the vector field of that region. As a consequence, we can predict the local evolutions (i.e., the behavior of the system inside each membrane) for all possible choices of initial multisets. We show some applications of this method to investigate the dynamics of two simple abstract toy-systems and of the Lotka-Volterra model.