On Stability and Equilibria of Analog Feedback Networks

A. Sherstinsky, Rosalind W. Picard


Both the analog Hopfield network [1] and the cellular neural network [2], [3] are special cases of the new M-lattice system, recently introduced to the signal processing community [4], [5], [6]. We prove that a subclass of the M-lattice is totally stable. This result also applies to the cellular neural network as a rigorous proof of its total stability. By analyzing the stability of fixed points, we derive the conditions for driving the equilibrium outputs of another subclass of the M-lattice to binary values. For the cellular neural network, this analysis is a precise formulation of an earlier argument based on circuit diagrams [2]. And for certain special cases of the analog Hopfield network, this analysis explains why the output variables converge to binary values even with non-zero neuron auto-connections. This behavior, observed in computer simulation by researchers for quite some time, is explained for the first time here. 1 Introduction The neurally-inspired network, introduced...

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