Combinatorial topology and qualitative dynamics in cellular neural networks
Pier Paolo Civalleri, Marco Gilli · 2002
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.