A topological description of the state space of a cellular neural network

The structure of the state space of cellular neural networks is investigated by putting the invariant manifolds of the fixed points of networks having the maximum number of equilibria in one-to-one correspondence with the cells of various orders of an n-cube (where n is the dimension of the state space) and of its dual. It is shown that the set of such networks is non-void for any template structure and that bifurcations of equilibria correspond to either vanishing or shrinking of cells in both complexes. Both topological representations provide an intuitive description of the geometrical features underlying the network dynamics