On dynamic behavior of weakly connected cellular neural networks

It was recently shown that weakly connected cellular neural/nonlinear networks (consisting of locally coupled oscillators) represent a suitable architecture for modelling biological neuro-computers. Such networks are described by large systems of nonlinear differential equations and may exhibit a rich dynamics, including chaos and complex bifurcation phenomena. We focus on space invariant cellular nonlinear networks and show that their dynamic behavior can be investigated through a spectral method, based on the application of the describing function technique. For a generic coupling, the spectral approach yields some approximate analytical conditions, that are useful for estimating some important network features and in particular for distinguishing between stationary (stable) and nonstationary behavior. In case of weak coupling the spectral method allows one to estimate the whole set of stable and unstable periodic limit cycles.