Stability and convergence analysis of model state variable trajectories of analogue KWTA neural circuit

A continuous-time mathematical model of K -winners-take-all (KWTA) neural circuit consisting of the state equation with discontinuous right-hand side and output equations is described. Stability and convergence analysis of the model state variable trajectories is performed by means of the Persidskij form of the state equation in conjunction with the associated Lyapunov function. According to analytical derivation the model is globally stable with a finite convergence time. The model can process any finite distinct signals with arbitrary specified minimal speed that is controlled by its single parameter. The model states do not depend on initial conditions and possess signal order preserving property. Simulation results confirm theoretical derivations and demonstrate good performance of the model.