Further results on convergence of cooperative standard cellular neural networks

The paper considers a class of nonsymmetric co operative standard cellular neural networks (SCNNs), which are defined by a cell-linking template, and are characterized by neuron activations modeled by a typical three-segment pwl function. The paper establishes conditions ensuring that the monotone solution semiflow associated to the considered class of SCNNs satisfies the Limit Set Dichotomy and is convergent toward equilibrium points. The conditions, which involve only static aspects of the equilibrium point configuration of the SCNNs, are easier to verify with respect to those in previous results in the literature. By means of a standard numerical program for locating the equilibrium points of pwl SCNNs, parameter ranges for which the conditions are verified, and the cooperative SCNNs are convergent, are established.