Combinatorial topology and qualitative dynamics in cellular neural networks

It is shown that the whole CNN invariant manifold structure can be described by the incidence relations between the cells of various orders of the n-dimensional cube and its dual polyhedron. The bifurcations of codimension 1 have a counterpart in transformations of the above geometrical structures due to shrinking or disappearing of specific cells. The geometrical interpretation allows us to predict some qualitative properties of a very general nature for the CNN dynamics.