Perturbations of CNNs

If a CNN template, through the application of one of the sign-changing transformations T defined by Chua and Wu (see Int. Journal of Circuit Theory and Applications, vol. 20, p.497-517, 1992), is positive and cell-linking and has isolated equilibria then the convergence of the original CNN follows; this is theorem 4 of the aforementioned paper. The main results of this paper use the condition of isolated equilibria. We show that it is possible to drop this requirement by demonstrating that having isolated equilibria is a generic condition on templates. Thus all templates can be perturbed slightly to a `close´ template, which has isolated equilibria. Perturbing templates allows us to consider the useful idea of making new sufficiently weak, cell connections in convergent CNN, so that the perturbed CNN is also convergent