Networks of Membranes

Abstract

In the systems considered in the previous chapters, the membrane structure corresponds to a cell-like structure, with the membranes arranged hierarchically. Such an arrangement is described by a tree. From a mathematical point of view it is then natural to consider related machineries whose underlying membrane structure is described by a graph of a given form, more restrictive or more general than a tree. More restrictive can be, for instance, a binary tree (each membrane directly contains two membranes), a linear tree (with all membranes arranged vertically, one into another), or a star (a tree with only two levels, hence with all internal membranes placed in the skin membrane). Because many universality results given in the previous chapters refer to systems with only two membranes, we implicitly have a sort of “normal form” in what concerns the underlying tree: of depth 2, linear.