Rich dynamics in weakly-coupled full-range cellular neural networks

The paper considers the full-range cellular neural networks (FRCNNs) when the neuron self-inhibiting nonlinearities are modelled by ideal hard comparator functions with two vertical straight segments. By using tools from the theory of differential inclusions, a time-scaling property for the trajectories of a family of FRCNNs depending upon a parameter ε is established. The significance of this property, which is not enjoyed by the familiar model of standard cellular networks, is discussed when ε is small in relation to the issue of the possible presence of rich non-convergent dynamics in weakly-coupled FRCNNs.