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A new dynamical system and computational circuit is described and analyzed. The dynamics permits the construction of a Lyapunov function that ensures global convergence to a unique stable equilibrium. The analog circuit realization is of the neural network type, with N cells represented by high-gain amplifiers, global feedback, and at most 2N interconnections, where N is the number of inputs. A specific application (called "the K-selector") which signals the ranks of the K largest elements of input list and, in parallel the rank of the (K+1)th element, is designed and numerically tested. For a given density of the input elements, one obtains feasible separation intervals of output signals, i.e., good processing performances. The circuit requires an appropriate control source and suitable scaling of the input data.