ON STABILITY AND EQUILIBRIA OF THE M-LATTICE

Both the analog Hopfield network [1] and the cellular neural network [ 2], [3] are special cases of the M-lattice system, recently introduced to the signal processing community [4]-[6], We prove that a subclass of the M-lattice is totally stable. This result also applies to the or iginal cellular neural network [2] as a rigorous proof of its total st ability. By analyzing the stability of fixed points, we derive the con ditions for driving the equilibrium outputs of another subclass of the M-lattice to binary values, For the cellular neural network, this ana lysis is a precise formulation of an earlier argument based on circuit diagrams [2], And for certain special cases of the analog Hopfield ne twork, this analysis explains why the output variables converge to bin ary values even with nonzero neuron auto-connections. This behavior, o bserved in computer simulation by researchers for quite some time, is explained for the first time here.