Simulation of Spatial P system models

Spatial P systems are an extension of the P systems formalism in which objects and membranes are embedded into a two-dimensional discrete space. Spatial P systems are characterised by the distinction between ordinary objects and mutually exclusive objects, with the constraint that any position can accommodate any number of ordinary objects, and at most one mutually exclusive object. The presence of mutually exclusive objects makes the simulation of Spatial P system models more complex than that of standard P systems. In this paper, we present a polynomial-time algorithm for the simulation of a restricted version of Spatial P systems where the restriction consists in considering only mutually exclusive objects and rules having exactly one reactant and one product. This version of Spatial P systems, although very restricted, is expressive enough to model interesting biological systems. In particular, we show how it can be used to simulate two models describing different dynamics of fish populations, namely the dynamics of territorial fish and the formation and movement of herring schools. In addition, the simulation methodology we propose can be adapted to simulate richer versions of Spatial P systems.