Dynamical aspects of P systems

A dynamical analysis of P systems is given that is focused on basic phenomena of biological relevance. After a short presentation of a new kind of P systems (PB systems), membrane systems with environment, called PBE systems, are introduced that are more suitable for modeling complex membrane interactions. Some types of periodicity and non-periodicity are considered for PBE systems by showing some "minimal" examples of systems that exhibit these properties. In particular, a discrete formulation of the Belousov-Zhabotinsky (BZ) reaction is given in terms of PBE systems. Some questions and open problems for future research are indicated.