On the stability analysis of cellular neural networks

The authors point out that by properly defining the Lyapunov function for the CNN, it can be proven that CNNs with opposite-sign template structure are completely stable for certain values of template values. Also, by using the Toeplitz-tridiagonal structure of the state matrices of CNNs with the positive-cell linking property, some conditions on the template values such that all trajectories of CNNs converge to stable equilibria can be obtained. A necessary and sufficient condition for the existence of an equilibrium point in each saturation region, partial saturation region, and linear region in which the CNN operates is obtained. This condition is valid not only for CNNs, but also for more general types of continuous-time neural network models. Finally, stable and unstable equilibrium points are determined