Equilibrium analysis of cellular neural networks

Cellular neural networks (CNNs) are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium-point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNNs, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements.